Question : Find the amount payable on maturity if INR 20,00,000 is invested at 12% per annum for $\frac{3}{2}$ years and interest is compounded half-yearly.
Option 1: INR 23,00,832
Option 2: INR 23,82,032
Option 3: INR 24,00,000
Option 4: INR 23,00,000
Correct Answer: INR 23,82,032
Solution :
Given: Principal = INR 20,00,000
Rate = 12% per annum
Time = $\frac{3}{2}$ years = 1.5 years
As given in the question, interest is compounded half-yearly.
$\therefore$ Rate = $\frac{12}{2}$ = 6%.
Time = 1.5 × 2 = 3 years
The amount payable on maturity
= $\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
= $2000000(1+\frac{6}{100})^3$
= $2000000\times(\frac{106}{100})^3$
= $2000000\times\frac{53}{50}\times\frac{53}{50}\times\frac{53}{50}$
= $2382032$
Hence, the correct answer is INR 23,82,032.
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