Question

If interest rate is unknown, give the formula for annual interest rate, j.

Answer 1

We have two cases below

1. Simple interest

$A=P(1+jn)$

where $A$ is the accumulated amount, $P$ is the principal amount, $j$ is interest rate and $n$ is the time period.

We can make $j$ subject of the formula to get the unknown interest rate $j$ as follows

$A=P(1+jn)$

$A=P+Pjn$

$P+Pjn=A$

$Pjn=A-P$

${Pjn\over Pn}={A-P\over Pn}$

$\therefore j={A-P\over Pn}$

2.Compound interest

$A=P(1+j)^n$

$P(1+j)^n=A$

${P(1+j)^n\over P}={A\over P}$

$(1+j)^n={A\over P}$

$(n\sqrt{1+j})^n=n\sqrt{{A\over P}}$

$1+j=n\sqrt{{A\over P}}$

$\therefore j=n\sqrt{{A\over P}}-1$