# SCHOOL OF SOCIAL SCIENCES

Course Name: FINANCIAL DERIVATIVES

Course Code: C39SN

# SEMESTER TWO – 2020/21

Take Home Exam

Duration: TWO HOURS

INSTRUCTIONS

SECTION B:    Answer EITHER Question B1 OR Question B2

Assume a 360-day year, unless otherwise stated.

Financial Tables are provided at the end of the examination paper.

SECTION A

The current share price of British Telecom (BT) is 460 pence. A European call option on the shares of the company has an exercise price of 480 pence and 180 days before it expires. The annual risk-free rate of interest is 4% and the annual standard deviation of the rate of return on the share is 20%.

The Black-Scholes-Merton Option Pricing Model for a European call option on a nondividend paying share is given by:

𝐶𝐶 = 𝑆𝑆𝑆𝑆(𝑑𝑑1) −𝐸𝐸𝑒𝑒−𝑟𝑟𝑟𝑟𝑆𝑆(𝑑𝑑2) where,

𝑆𝑆

ln𝐸𝐸+𝑟𝑟𝑟𝑟 + 𝜎𝜎√𝑟𝑟

𝑑𝑑1   =         𝜎𝜎

𝑑𝑑2   =     𝑑𝑑

C      =          theoretical value of the call option,

S      =            current (spot) price of the underlying asset,

E      =      exercise price of the option,

r        = annualized risk-free interest rate (continuously compounded),

𝜎𝜎       =         standard deviation of the underlying asset’s annual rate of return (continuously compounded). 𝜏𝜏            =         time to expiration (in years), e        =         2.71828 (the base of the natural logarithm),

ln      =      natural logarithm,

N(d) =       Cumulative Standard Normal Distribution value of ‘d’.

1. Compute the call option’s delta using the Black-Scholes-Merton Option Pricing Model, and in no more than 100 words outline the interpretations of this delta measure.
• marks)

1. Use the Black-Scholes-Merton model to calculate a theoretical value for this call option.

(20 marks)

1. If the call option in part b) is actually trading at 30 pence, describe in detail an arbitrage strategy to take advantage of the mispricing. (No more than 300 words).

(20 marks)

1. Use the actual call option price given in part c) together with the put-call parity to calculate a fair price of a synthetic put option that has the same exercise and time to maturity as the call option mentioned above.
• marks)

Continued on next page \…

1. Draw and fully annotate a graph of the profit at maturity of a straddle that is priced at fair value and constructed from the information given above. Use the graph to describe the characteristics of this straddle. (No more than 200 words).

(40 marks)

Total: 100 marks

Continued on next page \…

SECTION B

Answer EITHER Question B1 OR Question B2.

Question B1

1. a) A Malaysian company will be making a £50 million investment in the U.K. As a result, the company expects to receive semi-annual cash inflows in British Pounds and wishes to hedge against its currency exposure. Consequently, it enters into a 2-year fixed-for-fixed rate British Pound/Malaysian Ringgit currency swap with a principal value of £50 million.

At initiation, the exchange rate is RM5.50 per £. The counterparties of the swap have agreed on making semi-annual payments at a fixed rate of 3% on the Pound and 4% on the Ringgit.

Assume that the following exchange rates are observed at the initiation of the swap, where FXx,y denotes the value of the £ in terms of the Ringgit for a contract initiated at month x, with delivery at month y:

 Forward exchange rate in RM/£ FX0,6 5.40 FX0,12 5.30 FX0,18 5.20 FX0,24 5.00

In addition, you observe the following quotes for forward rate agreements (FRAs) on the Ringgit:

 FRA on Ringgit (% per annum) FRA0,6 4.2% FRA6,12 4.7% FRA12,18 4.8% FRA18,24 4.9%

1. Prepare a timeline clearly showing the payments and receipts on the swap from the perspective of the Malaysian company.
• marks)

1. Calculate the present value of the swap from the perspective of the Malaysian company.
• marks)

Continued on next page \…

1. b) A futures contract on a US Treasury Bill expires in 30 days. The Treasury Bill delivered by the futures contract has a maturity of 90 days. The quoted discount rates on US Treasury Bills (\$100 face value) are as follows:

30-day bill: 5.4% per annum

120-day bill: 5% per annum

1. Calculate the prices of the 30-day and the 120-day Treasury Bills.
• marks)

1. Calculate the fair price of the futures contract, and indicate whether the contract is over-priced or under-priced if it is actually trading in the market at \$98.04.
• marks)

• In no more than 200 words, explain what arbitrage transaction(s) could be executed to take advantage of any mispricing. Tabulate the arbitrage actions and the resulting cash flows.

(30 marks)

Total: 100 marks

Continued on next page \…

Question B2

1. Consider a hypothetical futures contract with a current price of \$100. The initial margin requirement is \$12, and the maintenance margin is \$10. You go long 20 contracts and meet all margin calls, but do not withdraw any excess margin.

1. What conditions would trigger a margin call in this setup? (No more than

100 words.)

(5 marks)

1. Copy the table below in your answer book, and complete the table assuming that the contract is purchased at the settlement (Futures) price of that day so that there is no marked-to-market profit or loss on the day of purchase.

(20 marks)

 Day Beginning Balance Funds Deposited Futures Price Price Change Gains/ Loss Ending Balance 0 – 100 – – 1 97 2 93 3 98 4 99 5 101

• How much are your total gains or losses by the end of day 5?

(5 marks)

1. A speculator has purchased two 3-month Eurodollar futures contracts at an index price of \$95.66 per contract. Each contract is based on a notional principal of \$1 million.

1. What is the annualised LIBOR rate priced into this contract?

(5 marks)

1. With a notional principal of \$1 million, what is the actual price of each futures contract?

(5 marks)

• A month later, the interest rate has changed to 5 percent. What is the new price of the futures contract?

(10 marks)

1. At 5 percent interest rate, how much is the speculator’s total gain or loss in dollar terms?

(5 marks) Continued on next page \…

1. A Malaysian company has a comparative advantage to borrowing in the Malaysian bond market rather than in the UK, but needs to finance a Pound Sterling investment in a UK project. Assume that the current exchange rate is 8 Ringgit/£, and that the company wants to borrow £50million over five years. The company can borrow an equivalent amount in Malaysian Ringgit (MR) at 5% coupon. Assume a flat term structure of interest rates and that interest rates (annual yields-to-maturity) for five-year default free bonds are 7% in the UK and 5% in Malaysia.

1. Consider a swap agreement in which the company might be interested in entering. What would be the current value of such a swap? Show your calculations.

(20 marks)

1. If at the end of the first year interest rates are 6% in the UK and 8% in Malaysia and the exchange rate is 7.5 MR/£, what is the MR and £ values of the swap for the party paying Ringgit and receiving Sterling?

(20 marks)

• What are the MR and £ values of the swap for the counter party?

(5 marks)

Total: 100 marks

– END OF EXAM PAPER –

Financial Tables

1. Cumulative Standard Normal Distribution (N(d) for positive and negative d)
2. Present Value Interest Factor (PVIF).
3. Future Value Interest Factor (FVIF).
4. Present Value Interest Factor of Ordinary Annuity (PVIFA)
5. Future Value Interest Factor of Ordinary Annuity (FVIFA)

Page

Cumulative Standard Normal Distribution Table

N(d) For             Positive  d                                                                                                                          N(d) For               Negative   d

 d 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 d -0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 0.00 0.5 0.504 0.508 0.512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359 0.00 0.5 0.496 0.492 0.488 0.484 0.4801 0.4761 0.4721 0.4681 0.4641 0.10 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 -0.10 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.20 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 -0.20 0.4207 0.4168 0.4129 0.409 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.30 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 -0.30 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.352 0.3483 0.40 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879 -0.40 0.3446 0.3409 0.3372 0.3336 0.33 0.3264 0.3228 0.3192 0.3156 0.3121 0.50 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224 -0.50 0.3085 0.305 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.281 0.2776 0.60 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 -0.60 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.70 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 -0.70 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.80 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 -0.80 0.2119 0.209 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.90 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389 -0.90 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.166 0.1635 0.1611 1.00 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 -1.00 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 1.10 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 -1.10 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.123 0.121 0.119 0.117 1.20 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.9015 -1.20 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.102 0.1003 0.0985 1.30 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 -1.30 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 1.40 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 -1.40 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.50 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 -1.50 0.0668 0.0655 0.0643 0.063 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 1.60 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 -1.60 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 1.70 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 -1.70 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.80 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 -1.80 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.90 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 -1.90 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.025 0.0244 0.0239 0.0233 2.00 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 -2.00 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 2.10 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 -2.10 0.0179 0.0174 0.017 0.0166 0.0162 0.0158 0.0154 0.015 0.0146 0.0143 2.20 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 -2.20 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.011 2.30 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 -2.30 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 2.40 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 -2.40 0.0082 0.008 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 2.50 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 -2.50 0.0062 0.006 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 2.60 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 -2.60 0.0047 0.0045 0.0044 0.0043 0.0041 0.004 0.0039 0.0038 0.0037 0.0036 2.70 0.9965 0.9966 0.9967 0.9968 0.9969 0.997 0.9971 0.9972 0.9973 0.9974 -2.70 0.0035 0.0034 0.0033 0.0032 0.0031 0.003 0.0029 0.0028 0.0027 0.0026 2.80 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.998 0.9981 -2.80 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.002 0.0019 2.90 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 -2.90 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 3.00 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.999 -3.00 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.001 0.001

Page

Present Value Interest Factor – PVIF(i %,n) of \$1 to be received at end of n periods at i %

 Period 1% 2% 0.980 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 0.855 18% 19% 20% 1 0.990 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.833 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 5 0.951 0.906 0.888 0.837 0.790 0.784 0.747 0.713 0.681 0.650 0.596 0.621 0.593 0.567 0.543 0.519 0.456 0.497 0.476 0.456 0.390 0.402 6 0.942 0.746 0.705 0.666 0.630 0.564 0.535 0.507 0.480 0.432 0.410 0.335 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 10 0.905 0.820 0.804 0.676 0.614 0.558 0.508 0.463 0.422 0.388 0.386 0.352 0.322 0.295 0.270 0.237 0.247 0.227 0.208 0.178 0.162 11 0.896 0.585 0.527 0.475 0.429 0.350 0.317 0.287 0.261 0.215 0.195 0.135 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 15 0.861 0.743 0.728 0.481 0.417 0.362 0.315 0.275 0.252 0.239 0.209 0.183 0.160 0.140 0.123 0.123 0.108 0.095 0.081 0.074 0.065 16 0.853 0.458 0.394 0.339 0.292 0.218 0.188 0.163 0.141 0.107 0.093 0.054 17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 20 0.820 0.673 0.610 0.456 0.377 0.312 0.258 0.215 0.178 0.116 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.020 0.031 0.026 25 0.780 0.295 0.233 0.184 0.146 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.010 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 35 0.706 0.500 0.355 0.253 0.181 0.130 0.094 0.068 0.049 0.036 0.026 0.019 0.014 0.010 0.008 0.006 0.004 0.003 0.002 0.002 40 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001 50 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0.009 0.005 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000

Future Value Interest Factor – FVIF(i %,n) of \$1 after n periods at i %,

 Period 1%      2%      3%      4%     5% 1.010  1.020                         1.050 6% 7% 8% 1.080 9% 10% 11% 12% 1.120 13% 14% 15% 16% 17% 18% 19% 20% 1 1.060 1.070 1.100 1.110 1.150 1.160 1.170 1.180 1.190 1.200 2 1.020  1.040  1.061  1.082  1.103 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 3 1.030  1.061  1.093  1.125  1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 4 1.041  1.082  1.126  1.170  1.216 1.262 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 5 1.051  1.104                         1.276 1.062  1.126  1.194  1.265  1.340 1.338 1.403 1.469 1.587 1.611 1.685 1.762 1.974 2.082 2.195 2.011 2.100 2.192 2.288 2.386 2.488 6 1.419 1.501 1.772 1.870 2.313 2.436 2.565 2.700 2.840 2.986 7 1.072  1.149  1.230  1.316  1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 8 1.083  1.172  1.267  1.369  1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300 9 1.094  1.195  1.305  1.423  1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 10 1.105  1.219                         1.629 1.116  1.243  1.384  1.539  1.710 1.791 1.967 2.159 2.332 2.594 2.839 3.106 3.479 4.046 4.411 4.807 5.234 5.695 6.192 11 1.898 2.105 2.853 3.152 4.652 5.117 5.624 6.176 6.777 7.430 12 1.127  1.268  1.426  1.601  1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916 13 1.138  1.294  1.469  1.665  1.886 2.133 2.410 2.720 3.066 3.452 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 14 1.149  1.319  1.513  1.732  1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.261 7.076 7.988 9.007  10.147 11.420 12.839 15 1.161  1.346                         2.079 1.173  1.373  1.605  1.873  2.183 2.397 2.759 3.172 3.426 4.177 4.785 5.474 6.130 8.137 9.266 13.590 15.407 16 2.540 2.952 4.595 5.311 9.358 10.748 18.488 17 1.184  1.400  1.653  1.948  2.292 2.693 3.159 3.700 4.328 5.054 5.895 6.866 7.986 9.276  10.761 12.468  14.426  16.672  19.244 22.186 18 1.196  1.428  1.702  2.026  2.407 2.854 3.380 3.996 4.717 5.560 6.544 7.690 9.024  10.575  12.375 14.463  16.879  19.673  22.901 26.623 19 1.208  1.457  1.754  2.107  2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613  10.197  12.056  14.232 16.777  19.748  23.214  27.252 31.948 20 1.220  1.486                         2.653 1.282  1.641  2.094  2.666  3.386 3.207 3.870 4.661 6.848 6.727 8.062 9.646                              16.367 19.461 38.338 25 4.292 5.427 10.835 13.585  17.000  21.231  26.462  32.919 40.874  50.658  62.669  77.388 95.396 30 1.348  1.811  2.427  3.243  4.322 5.743 7.612  10.063  13.268  17.449 22.892  29.960  39.116  50.950  66.212 85.850  111.065  143.371  184.675  237.376 35 1.417  2.000  2.814  3.946  5.516 7.686  10.677  14.785  20.414  28.102 38.575  52.800  72.069  98.100  133.176 180.314  243.503  327.997  440.701  590.668

Present Value Interest Factor of Ordinary Annuity –  PVIFA(i %,n) of \$1 per period (in arrear) at i % for n periods

 Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 0.855 18% 19% 20% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.833 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.589 3.498 3.410 2.991 6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 3.998 3.889 3.784 3.685 3.326 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.836 4.656 4.486 4.192 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 5.687 5.453 5.234 5.029 4.327 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 14 13.004 12.106 11.296  10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 15 13.865 13.578 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.405 5.162 4.938 4.675 16 14.718 12.561  11.652  10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 6.604 6.265 5.954 5.668 4.730 17 15.562 14.292 13.166  12.166  11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 6.729 6.373 6.047 5.749 5.475 5.222 4.990 4.775 18 16.398 14.992 13.754  12.659  11.690 10.828  10.059 9.372 8.756 8.201 7.702 7.250 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812 19 17.226 15.678 14.324  13.134  12.085 11.158  10.336 9.604 8.950 8.365 7.839 7.366 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843 20 18.046 19.523 12.462 11.470  10.594 9.818 9.129 8.514 7.963 7.469 7.025 6.623 6.259 5.929 5.628 5.766 5.467 5.195 4.870 25 22.023 17.413  15.622  14.094 12.783  11.654  10.675 9.823 9.077 8.422 7.843 7.330 6.873 6.464 6.097 4.948 30 25.808 22.396 19.600  17.292  15.372 13.765  12.409  11.258  10.274 9.427 8.694 8.055 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.979 35 29.409 24.999 21.487  18.665  16.374 14.498  12.948  11.655  10.567 9.644 8.855 8.176 7.586 7.070 6.617 6.215 5.858 5.539 5.251 4.992 40 32.835 27.355 23.115  19.793  17.159 15.046  13.332  11.925  10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 50 39.196 31.424 25.730  21.482  18.256 15.762  13.801  12.233  10.962 9.915 9.042 8.304 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999

Future Value Interest Factor of Ordinary Annuity – FVIFA(i,n)  of \$1 per period (in arrear) at i % for n periods

 Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100 2.110 2.120 2.130 2.140 2.150 2.160 2.170 2.180 2.190 2.200 3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310 3.342 3.374 3.407 3.440 3.473 3.506 3.539 3.572 3.606 3.640 4 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.710 4.779 4.850 4.921 4.993 5.066 5.141 5.215 5.291 5.368 5 5.101 5.204 5.309 5.416 5.526 5.637 5.751 5.867 5.985 6.105 6.228 6.353 6.480 6.610 6.742 6.877 7.014 7.154 7.297 7.442 6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716 7.913 8.115 8.323 8.536 8.754 8.977 9.207 9.442 9.683 9.930 7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 9.783  10.089  10.405  10.730  11.067 11.414  11.772  12.142  12.523  12.916 8 8.286 8.583 8.892 9.214 9.549 9.897  10.260  10.637  11.028  11.436 11.859  12.300  12.757  13.233  13.727 14.240  14.773  15.327  15.902  16.499 9 9.369 9.755  10.159  10.583  11.027 11.491  11.978  12.488  13.021  13.579 14.164  14.776  15.416  16.085  16.786 17.519  18.285  19.086  19.923  20.799 10 10.462  10.950  11.464  12.006  12.578 13.181  13.816  14.487  15.193  15.937 16.722  17.549  18.420  19.337  20.304 21.321  22.393  23.521  24.709  25.959 11 11.567  12.169  12.808  13.486  14.207 14.972  15.784  16.645  17.560  18.531 19.561  20.655  21.814  23.045  24.349 25.733  27.200  28.755  30.404  32.150 12 12.683  13.412  14.192  15.026  15.917 16.870  17.888  18.977  20.141  21.384 22.713  24.133  25.650  27.271  29.002 30.850  32.824  34.931  37.180  39.581 13 13.809  14.680  15.618  16.627  17.713 18.882  20.141  21.495  22.953  24.523 26.212  28.029  29.985  32.089  34.352 36.786  39.404  42.219  45.244  48.497 14 14.947  15.974  17.086  18.292  19.599 21.015  22.550  24.215  26.019  27.975 30.095  32.393  34.883  37.581  40.505 43.672  47.103  50.818  54.841  59.196 15 16.097  17.293  18.599  20.024  21.579 23.276  25.129  27.152  29.361  31.772 34.405  37.280  40.417  43.842  47.580 51.660  56.110  60.965  66.261  72.035 16 17.258  18.639  20.157  21.825  23.657 25.673  27.888  30.324  33.003  35.950 39.190  42.753  46.672  50.980  55.717 60.925  66.649  72.939  79.850  87.442 17 18.430  20.012  21.762  23.698  25.840 28.213  30.840  33.750  36.974  40.545 44.501  48.884  53.739  59.118  65.075 71.673  78.979  87.068  96.022  105.93 18 19.615  21.412  23.414  25.645  28.132 30.906  33.999  37.450  41.301  45.599 50.396  55.750  61.725  68.394  75.836 84.141  93.406  103.74 115.27 128.12 19 20.811  22.841  25.117  27.671  30.539 33.760  37.379  41.446  46.018  51.159 56.939  63.440  70.749  78.969  88.212 98.603  110.28 123.41 138.17 154.74 20 22.019  24.297  26.870  29.778  33.066 36.786  40.995  45.762  51.160  57.275 64.203  72.052  80.947  91.025  102.44 115.38 130.03 146.63 165.42 186.69 25 28.243  32.030  36.459  41.646  47.727 54.865  63.249  73.106  84.701  98.347 114.41 133.33 155.62 181.87 212.79 249.21 292.10 342.60 402.04 471.98 30 34.785  40.568  47.575  56.085  66.439 79.058  94.461  113.28 136.31 164.49 199.02 241.33 293.20 356.79 434.75 530.31 647.44 790.95 966.71 1,181.9 35 41.660  49.994  60.462  73.652  90.320 111.43 138.24 172.32 215.71 271.02 341.59 431.66 546.68 693.57 881.17 1,120.7  1,426.5  1,816.7  2,314.2  2,948.3 40 48.886  60.402  75.401  95.026  120.80 154.76 199.64 259.06 337.88 442.59 581.83 767.09 1,013.7  1,342.0  1,779.1 2,360.8  3,134.5  4,163.2  5,529.8  7,343.9 50 64.463  84.579  112.80 152.67 209.35 290.34 406.53 573.77 815.08 1,163.9 1,668.8  2,400.0  3,459.5  4,994.5  7,217.7 10,436 15,090 21,813 31,515 45,497