Question : If interest is being compounded half yearly and the rate of interest is 20 percent per annum, then in how much time Rs. 15,000 will become Rs. 19,965 at compound interest?
Option 1: 12 months
Option 2: 30 months
Option 3: 24 months
Option 4: 18 months
Correct Answer: 18 months
Solution :
Given: The interest is being compounded half yearly and the rate of interest is 20 percent per annum.
Use the formula, $A=P[1+\frac{R}{n}]^{nt}$ where $A$, $P$, $R$, $n$, and $t$ are the amount, principal, rate, number of times interest applied per period and number of periods elapsed.
$19965=15000[1+\frac{20}{100\times 2}]^{2t}$
⇒ $\frac{19965}{15000}=[1+\frac{20}{100\times 2}]^{2t}$
⇒ $(\frac{11}{10})^3=[1+\frac{1}{10}]^{2t}$
⇒ $(\frac{11}{10})^3=(\frac{11}{10})^{2t}$
⇒ $2t=3$
⇒ $t=\frac{3}{2}$ years
⇒ $t=\frac{3}{2}\times 12=18$ months
Hence, the correct answer is 18 months.
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