In how many years will a sum of ₹ 800 at 10 % per annum compound interest, compounded semiannually

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6.Interest

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In how many years will a sum of ₹ $800$ at $10 \%$ per annum compound interest, compounded semiannually becomes ₹ $926.10$?

A

$1.5$

B

$1.0$

C

$2.5$

D

$2.0$

Solution

(a) Rate of interest $=10 \%$ per annum. So, rate of interest for half-yearly $=5 \%$ Therefore, $A=P \frac{(1+R)^{T}}{100}$

$926.10=800 \frac{(1+5)^{T}}{100}$

$926.10=800 \frac{(100+5)^{T}}{100}$

$926.10=800 \frac{(21)^{T}}{20}$

$\frac{926.1 \times 10}{8000 \times 10}=\left(\frac{21}{20}\right)^{T}$

$\frac{9261}{8000}=\left(\frac{21}{20}\right)^{T}$

$\left(\frac{21}{20}\right)^{3}=\left(\frac{21}{20}\right)^{T}$

Hence, time $=3$ half-years

$=1 \frac{1}{2}$ years

Standard 13

Quantitative Aptitude

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