Question

Use the appropriate compound interest formula to find the amount that will be in each account, given the stated conditions.$45,000 invested at 5% annual interest for 7 years compounded (a) annually; (b) semiannually. Do not round until the final answer. Then round to the nearest cent as needed

Answer 1

The value of principal amount is P=45000.

The value of rate of interest is R=5%.

The time is n=7 years.

The formula for the amount when interest is compounded annually is,

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

Substitute the values in the formula to obtain the value of amount.

$\begin{gathered} A=(45000)(1+\frac{5}{100})^7 \\ =(45000)(1.05)^7_{} \\ =63319.52 \end{gathered}$

So amount if intrest is compouned annually is $63319.52.

The formula for amount when interest is coumpounded semi annualy is,

$A=P(1+\frac{R}{200})^{2n}$

Substitute the known values in the formula to obtain the value of amount.

$\begin{gathered} A=(45000)(1+\frac{5}{200})^{2\cdot7} \\ =(45000)(1.025)^{14} \\ =63583.822 \end{gathered}$

So amount if intrest is compouned semi-annually is $63583.822.