A loan $P$ is repaid in $n$ equal instalments by the reducing-balance method, at rate $i$ per instalment period. Which formula gives the instalment $E$ ?

E = \frac{P\,i}{(1 + i)^{n} - 1}

Correct answerYour answer

E = \frac{P(1 + ni)}{n}

Correct answerYour answer

E = P\,i\,(1 + i)^{n}

Correct answerYour answer

E = \frac{P\,i\,(1 + i)^{n}}{(1 + i)^{n} - 1}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The instalments are an annuity whose present value is the loan: $E \times \frac{1 - (1 + i)^{-n}}{i} = P$ .
So $E = \frac{P\,i}{1 - (1 + i)^{-n}} = \frac{P\,i\,(1 + i)^{n}}{(1 + i)^{n} - 1}$ .

Worth noting

$\frac{P(1 + ni)}{n}$ is the flat-rate instalment.

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A loan PPP is repaid in nnn equal instalments by the reducing-balance method, at rate iii per instalment period. Which formula gives the instalment EEE?