Question

Find the amount and compound interest on ₹10,000 for $1\frac{1}{2}$ years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Answer 1

Principal (P) = ₹10,000
Rate (R) = 10% per annum = 5% per half year
Number of years (n) $=1\frac{1}{2}$ years = 3 half years
Amount (A) $=P{(1+\frac{R}{100})}^n$
$=[10,000{(1+\frac{5}{100})}^3]$
$=[10,000{(1+\frac{1}{20})}^3]$
$=[10,000{\left(\frac{21}{20}\right)}^3]$
$=₹11,576.25$

C.I. = A.P = ₹(11,576.25 - 10,000) = ₹1,576.25

The amount of 1 year and 6 months can be calculated by first calculating amount for 1 year using compound interest and then calculate amount for 6 months using simple interest.
Amount for first 1 year,
$A=P{(1+\frac{R}{100})}^n$
$=[10,000{(1+\frac{10}{100})}^1]$
$=[10,000{(1+\frac{1}{10})}^1]$
$=[10,000{\left(\frac{11}{10}\right)}^1]$
$=₹11,000$

By taking ₹11,000 as principal, the S.I. for the next $\frac{1}{2}$ year will be calculated.
$S.I.=\frac{P\times R\times T}{100}=\frac{11,000\times \frac{1}{2}\times 10}{100}=₹550$
Interest for the first 1 year = ₹(11,000 – 10,000) = ₹1,000
∴ Total C.I. = ₹(1,000 + 550) = ₹1,550
Thus, the interest would be more when compounded half yearly than the
interest when compounded annually.