Question

8) $14,000 invested at 7% compounded semiannually after a period of 12 yearsF) $31,530.68G) $17.966.6H) $30,885.60J) $31,966.60

Answer 1

Consider that the amount is given by,

`A=P(1+r)^n`

Here, 'P' is the principal, 'n' is the number of compounding periods, 'r' is the effective rate of interest per period.

Given that compounding is done semiannually i.e. twice a year, so the number of periods in 12 years will be 24,

`n=2*12=24`

The effective rate of interest is given by,

`r=(7)/(2*100)=0.035`

Substitute the values and solve for the amount as follows,

`\begin{gathered} A=14000(1+0.035)^(24) \\ A=14000*2.28 \\ A=31966.60 \end{gathered}`

Thus, the required amount will be $31966.60

Therefore, option J is the correct choice.