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# Find the amount which Ram will get on Rs 4,096 if he gave it for 18 months at 12.5% per annum, interest being compounded half yearly.

9  Find the amount which Ram will get on Rs 4,096 if he gave it for 18 months at  $12\frac{1}{2}$ % per annum, interest being compounded half-yearly.

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Given,

Principal amount, P = Rs 4,096

Rate of interest, R

$R =12\frac{1}{2} \% = \frac{25}{2} \% p.a. =\frac{25}{4} \% \ half\ yearly$

Time period, n = 18 months = (12 + 6) months = 1.5 years = 3 half years

(There are 3 half years in 1.5 years)

We know,

Amount when interest is compounded annually, (A)

$A =P(1+\frac{R}{100})^n$

Therefore, the required amount

$=4096(1+\frac{25}{4\times100})^{3} = 4913$

$\therefore$ Ram will get Rs 4,913 after 18 months.

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