Question

37. PROBLEM SOLVING You deposit $5000 in an account that pays 2.25% annual interest. Find the balance after 5 years when the interest is compounded quarterly.Solution: $5593.60

Answer 1

Final amount with compound interest is:

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

P is the principal amount

r is the interest rate in decimal form (%/100)

n is the number o times compounded

t is the time in years

For the given situation:

`\begin{gathered} P=5,000 \\ r=(2.25)/(100)=\text{0}.0225 \\ n=4(quarterly) \\ t=5 \\ \\ A=5,000(1+(0.0225)/(4))^(4\cdot5) \\ \\ A=5,000(1+(0.0225)/(4))^(20) \\ \\ A\approx5,593.60 \end{gathered}`

Then, the balance after 5 years (final amount) is $5,593.60