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+(R)/(100))^n`

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

`\begin{gathered} A=(45000)(1+(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+(R)/(200))^(2n)`

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

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

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