Question

Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps.Principal Rate Compounded Time$580 4.65% Quarterly6 yearsThe future value is $and the compound interest is $ХSCheck

Answer 1

Compound Interest

The Future Value of investment on compound interest can be calculated with the formula:

`FV=PV(1+i)^n`

Where PV is the present value or Principal, i is the adjusted interest rate and n is the number of compounding periods.

The principal is PV=$580.

The APR is 4.65% = 0.0465

The compounding period is quarterly.

Since there are 4 quarters in a year, the adjusted interest rate is:

i = 0.0465 / 4 = 0.011625.

The number of periods is n=6 years * 4 = 24 quarters

Now compute the future value:

`FV=580(1+0.011625)^(24)`

Calculating:

`\begin{gathered} FV=\$580\cdot1.31968 \\ FV=\$765.42 \end{gathered}`

The future value is $765.42 and the present value is $580, so the interest is:

I = $765.42 - $580

I = $185.42