Interest Formulas and Cash Flow Questions and Answers

Answer: A

Correct answer: F, given P

The notation reads as a fraction: the quantity before the slash is what is being found and the one after it is what is known. So \( (F/P, i, n) \) finds a future sum from a present one, and multiplying P by it gives F. Reading the pair the other way round is the commonest error in using the tables.

Answer: B

Correct answer: a uniform series into a present sum

\( (P/A, i, n) \) finds P given A, so it converts a uniform series into the single present sum equivalent to it. Its reciprocal, \( (A/P) \), goes the other way and is the capital recovery factor. Every factor has this paired character, which halves the number that need be remembered.

Answer: C

Correct answer: \( (A/P, i, n) \)

Capital recovery is the annual amount that repays a present sum with interest over n periods, so it finds A given P. It is the factor behind every loan instalment and every annual equivalent of a capital cost, and it is the reciprocal of the series present worth factor.

Answer: D

It gives the annual deposit needed to accumulate a stated future sum, which is how a replacement or sinking fund is sized in practice. Its reciprocal is the series compound amount factor, which works the calculation the other way.

Answer: A

Correct answer: the interest rate i

The identity is \( (A/P, i, n) = (A/F, i, n) + i \). The reasoning is direct: to recover a present sum you must both pay the interest on it each period, which is \( iP \), and accumulate the principal itself by the end, which is the sinking fund deposit. The two together are the capital recovery amount.

Answer: B

Discounting and compounding a single sum are exact inverses, so the two factors multiply to unity. The series factors pair off in the same way, present worth with capital recovery and compound amount with sinking fund.

Answer: C

Correct answer: one period before the first payment

This is the convention that causes most of the errors in using the factor. The series present worth factor discounts the payments to the period immediately preceding the first of them, not to the date of the first payment. For an ordinary series beginning at the end of year one, that period is time zero, which is why it usually works out conveniently.

Answer: D

Correct answer: the fifth deposit

The series compound amount factor accumulates the deposits to the date of the last one, not to a period beyond it. So five annual deposits give a sum located at the fifth deposit, with no interest earned on that final deposit. Placing it a year later is the mirror image of the mistake made with the present worth factor.

Answer: A

The series factor places the value one period before the first payment, which is somewhere in the middle of the horizon, so a single-payment present worth factor brings it the rest of the way. Two factors in sequence handle any shifted series.

Answer: B

Correct answer: indefinitely

A perpetuity continues without end, and its present worth converges because later payments are discounted so heavily that the series has a finite sum: \( P = A/i \). It is the model for anything treated as permanent - an endowment, a bridge maintained for ever - and the simplicity of the formula is why the idealisation is used.