Interest Formulas and Cash Flow Questions and Answers

Answer: A

Correct answer: costs rising by 5 per cent each year

A constant percentage is a geometric gradient, each term a fixed multiple of the last. An arithmetic gradient rises by a constant amount, which is what the other three describe - 500 a year, a fixed annual increment, and the series rising by 200 each time. The distinction matters because the two use quite different factors.

Answer: B

Correct answer: time zero

The series present worth factor places its result one period before the first payment. With the first payment at the end of year one, that period is time zero, so the answer is already the present worth and no further discounting is needed - but neither may it be reported as a value at the end of year one, which would overstate it by a year’s interest.

Answer: C

Correct answer: too low, part of each payment having been interest

Each instalment is divided between interest and principal, and only the principal part reduces the balance. Subtracting the whole of every payment therefore credits the borrower with more repayment than has occurred, and the balance reported is below the truth. The correct figure is the present worth of the payments still to be made.

Answer: D

The sinking fund part accumulates the capital back and the interest term services it in the meantime, so the two together are exactly what recovery requires. The identity is the quickest way to get one factor from the other.

Answer: A

The convention is indeed the basis of the derivation, but it places the future worth at the date of the last payment, which earns no interest. It is the series present worth that sits one period outside the series, at the front.

Answer: B

Correct answer: inflation, as a constant percentage

A geometric gradient models a constant proportional increase, which is exactly what a general inflation rate is: each year’s cost is a fixed multiple of the last. A cost rising by a constant absolute amount - a maintenance charge growing by 500 a year with wear - is an arithmetic gradient instead.

Answer: C

Inverting the notation gives the reciprocal, so P over A pairs with A over P and nothing else. The other three pairings do not invert into one another and their products are not unity, so neither can substitute for the other.