Question

Arif took a loan of ₹80,000 from a bank. If the rate of interest is 10% per annum, find the difference in
(A) Compounded yearly.
(B) Compounded half yearly.

Answer 1

First we calculate the amount for 1 year using the formula of compound interest after that we calculate amount for 6 months using simple interest formula.
Amount for 1 year,
$\therefore$ Amount (A) $=P{(1+\frac{R}{100})}^n$
$=[80,000{(1+\frac{1}{10})}^1]$
$=[80,000{\left(\frac{11}{10}\right)}^1]$
$=₹88,000$

By using ₹88,000 as principal, the S.I. for the next $\frac{1}{2}$ year will be calculated.

$SI=\frac{P\times R\times T}{100}=\frac{88,000\times \frac{1}{2}\times 10}{00}=₹4400$

Case 1: Compounded yearly
$\therefore$ Interest for the first year = ₹(88,000 - 80,000) = ₹8,000
And the interest for the next $\frac{1}{2}$ year = ₹4,400
$\therefore$ Total C.I. = ₹(8,000 + 4,400) = ₹12,400

Amount (A) = P + C.I. = ₹(80,000 + 12,400)
Amount (A) = P + C.I. = ₹92,400

Case 2: Compounded half yearly
Amount (A) = P + C.I. = ₹(80,000 + 12,400)
Rate (R) = 10% per annum = 5% per half annum
The interest is compounded half yearly
There will be 3 half years in $1\frac{1}{2}$ years.
Amount (A) $=P{(1+\frac{R}{100})}^n$
$=[80,000{(1+\frac{5}{100})}^3]$
$=[80,000{\left(\frac{105}{100}\right)}^3]$
$=₹92,610$

∴ Difference between the amounts = ₹(92,610 – 92,400) = ₹210