What sum invested for $1\dfrac{1}{2}$ years compounded half-yearly at the rate of 4% p.a. will amount to ₹132651?

Let principal = P.

Given, A = ₹132651.

Since interest is compounded half-yearly,

rate = $\dfrac{4}{2}$% = 2%.

n (the number of conversion periods) = 3.

We know,

A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Putting values in formula we get,

$132651 = P\Big(1 + \dfrac{2}{100}\Big)^3 \\[1em] 132651 = P\Big(\dfrac{102}{100}\Big)^3 \\[1em] 132651 = P\Big(\dfrac{51}{50}\Big)^3 \\[1em] 132651 = P \times \dfrac{132651}{125000} \\[1em] P = \dfrac{132651 \times 125000}{132651} \\[1em] P = ₹125000.$

Hence, ₹125000 will amount to ₹132651 in $1\dfrac{1}{2}$ year at 4% per annum compounded semi-annually.