A money lender lent out Rs. 10000 for 2 years at 16% per annum, the interest being compounded annually. How much more he could earn if the interest be compounded half-yearly?

Given:

P = Rs. 10000

T = 2 years

R = 16% p.a

To find: Here we have to find the extra amount money lender could have earned if the interest be compounded half-yearly.

Solution:

Interest is compounded half-year yearly. Then,

Rate (r) = $\frac{16}{2} = 8%

And he will take an interest after every 6 months so we have

Time (n) = 4

$A\ =\ p\left( 1\ +\ \frac{r}{100}\right)^{n}$

$A\ =\ 10000\left( 1\ +\ \frac{8}{100}\right)^{4}$

$A\ =\ 10000\left(\frac{100\ +\ 8}{100}\right)^{4}$

$A\ =\ 10000\left(\frac{108}{100}\right)^{4}$

$A\ =\ 10000\ \times \ ( 1.08)^{4}$

$A\ =\ 10000\ \times \ 1.360$

$A\ =\ Rs.\ 13600$

Now if he gives it on 16% p.a:

Rate (R) = 20%

Time (N) = 2

$A\ =\ 10000\ \times \ \left( 1\ +\ \frac{16}{100}\right)^{2}$

$A\ =\ 10000\ \times \ \left(\frac{100\ +\ 16}{100}\right)^{2}$

$A\ =\ 10000\ \times \ \left(\frac{116}{100}\right)^{2}$

$A\ =\ 10000\ \times \ ( 1.16)^{2}$

$A\ =\ 10000\ \times \ 1.345$

$\mathbf{A\ =\ Rs.\ 13450}$

The extra money he could earn = Rs. 13,600 $-$ 13450 = Rs. 150

So, Money lander could have earned Rs. 150 more if the interest be compounded half-yearly.

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