Question : At what rate of compound interest per annum, a sum of Rs. 20,000 becomes Rs. 23,152.50 in 1 year and 6 months compounded half-yearly?
Option 1: 10% per annum
Option 2: 5% per annum
Option 3: 12% per annum
Option 4: 8% per annum
Correct Answer: 10% per annum
Solution :
Given: At what rate of compound interest per annum, a sum of Rs. 20,000 becomes Rs. 23,152.50 in 1 year and 6 months compounded half-yearly
Here Principle ($P$) = Rs. 20,000
Amount ($A$) = Rs. 23,152.50
Time = 1 year 6 months = 1.5 years
Let, the rate of interest = $r$%
Condition = Compounded half-yearly
So, the new rate($R$) = $\frac{r}{2}$% and the new time($T$) = 1.5 × 2 = 3 years
We know that, $A = P(1+\frac{R}{100})^T$
⇒ $23152.50 = 20000(1+\frac{\frac{r}{2}}{100})^3$
⇒ $(1+\frac{r}{200})^3=\frac{23152.50}{20000}$
⇒ $(1+\frac{r}{200})^3=(\frac{21}{20})^3$
⇒ $1+\frac{r}{200}=\frac{21}{20}$
⇒ $r=10$%
Hence, the correct answer is 10% per annum.
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