Question

Find the amount that the daily worker Ram Singh would receive if he invests Rs. 8,192 for 18 months at 12 ½ % per annum, the interest being compounded half yearly.

Answer 1

$9826.

Explanation:

We are asked to find the amount that the the daily worker Ram Singh would receive if he invests Rs. 8,192 for 18 months at 12 ½% per annum and the interest is being compounded half yearly.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nT)`, where,

`A=\text{Final amount after T years}`,

`r=\text{Interest rate in decimal form}`,

`n=\text{Number of times interest in compounding per year}`,

`T=\text{Time in years}`.

Let us convert interest rate in decimal form.

`12 (1)/(2)\%=12.5\%=(12.5)/(100)=0.125`

As interest is compounded half-yearly, therefore, n will be 2.

1 year = 12 months,

18 months = 18/12 year = 1.5 year.

Upon substituting these values in compound interest formula we will get,

`A=8192(1+(0.125)/(2))^(2*1.5)`

`A=8192(1+0.0625)^(3)`

`A=8192(1.0625)^(3)`

`A=8192*1.199462890625`

`A=9826`

Therefore, the daily worker Ram Singh will receive $9826 after 18 months.