Interest Formulas and Cash Flow Questions and Answers

Answer: A

Correct answer: remaining payments

At any date the debt is worth what is still owed, and what is still owed is the present worth of the payments yet to be made, discounted at the loan rate. Subtracting the payments made from the original principal gives a figure that is too high, because part of each payment was interest and never touched the principal.

Answer: B

Correct answer: lowers the instalment but raises the total interest

A longer term spreads the same principal over more payments, so each is smaller; but the balance is outstanding for longer and interest accrues on it throughout, so the total paid rises. The trade is affordability against total cost, and it is the reason a long mortgage costs so much more than a short one.

Answer: C

Correct answer: 16 105

\[ F = 10\,000\,(1.10)^5 = 10\,000 \times 1.6105 = 16\,105. \] Simple interest would have given 15 000, and the difference of 1105 is the interest earned on interest - small over five years and dominant over thirty, which is the whole argument of compounding.

Answer: D

Correct answer: 62 paise

Discounting is the reciprocal of compounding: \[ \frac{1}{1.611} = 0.62. \] So a rupee five years away is worth about 62 paise today at ten per cent. This is why a project’s distant benefits count for so little and why the discount rate chosen has so large an effect on any long-lived comparison.

Answer: A

Correct answer: 6105

\[ F = 1000 \times \frac{(1.10)^5 - 1}{0.10} = 1000 \times 6.105 = 6105. \] Five deposits of 1000 total 5000, so the interest earned is 1105 - and note that the fifth deposit earns nothing, since the sum is located at its own date.

Answer: B

Correct answer: 3791

\[ P = 1000 \times \frac{1 - (1.10)^{-5}}{0.10} = 1000 \times 3.791 = 3791. \] The five payments total 5000 and are worth 3791 today, the difference being the interest the money would have earned in the meantime. The value belongs at time zero, one period before the first payment.

Answer: C

Correct answer: 13 190

\[ A = 50\,000 \times (A/P, 10\%, 5) = 50\,000 \times 0.2638 \] \[ = 13\,190. \] The five payments total 65 950 against 50 000 recovered, and the difference of 15 950 is the interest. Note the factor is a little above 0.20, since simple repayment of a fifth each year would ignore the interest entirely.

Answer: D

Correct answer: 1638

\[ A = 10\,000 \times (A/F, 10\%, 5) = 10\,000 \times 0.1638 \] \[ = 1638. \] The deposits total 8190 and the remaining 1810 is interest earned within the fund. The sinking fund factor is below 0.20 for the same reason the capital recovery factor is above it.

Answer: A

Correct answer: 26 380

\[ A = 100\,000 \times (A/P, 10\%, 5) = 100\,000 \times 0.2638 \] \[ = 26\,380. \] Over five years the borrower pays 131 900 for 100 000 borrowed, so 31 900 is interest - which is what the capital recovery factor is computing.

Answer: B

Correct answer: 10 000

Interest in any instalment is the rate applied to the balance outstanding at the start of the period, and at the outset that balance is the full principal: \[ 100\,000 \times 0.10 = 10\,000. \] The remaining 16 380 of the instalment repays principal, so the second year’s interest is charged on 83 620 and is correspondingly less.