Which formula gives the deposit $R$ to be made at the end of each period into a sinking fund so that it grows to $A$ after $n$ periods at rate $i$ a period?

R = \frac{A}{n}

Correct answerYour answer

R = \frac{A\,i}{1 - (1 + i)^{-n}}

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R = A(1 + i)^{n}

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R = \frac{A\,i}{(1 + i)^{n} - 1}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The deposits form an annuity whose amount must be $A$ : $R \times \frac{(1 + i)^{n} - 1}{i} = A$ .
Solving for $R$ : $R = \frac{A\,i}{(1 + i)^{n} - 1}$ .

Worth noting

$\frac{A\,i}{1 - (1 + i)^{-n}}$ is the instalment that repays a loan of $A$ taken today, an EMI, not a saving towards $A$ .

Ten questions from Perpetuity, Sinking Funds & Bonds, at your own pace.

Which formula gives the deposit RRR to be made at the end of each period into a sinking fund so that it grows to AAA after nnn periods at rate iii a period?