Question

Suppose the First Bank of Lending offers a CD (Certificate of Deposit) that has a 6.45% interest rate andis compounded quarterly for 3 years. You decide to invest $5500 into this CD.a) Determine how much money you will have at the end of three years.b) Find the APY.

Answer 1

In order to solve this, we have to use the compound interest formula given by the following expression:

$A=P(1+\frac{r}{n})^{nt}$

Where r is the interest rate, P is the initial amount deposited, n the number of times the period is compounded a year, t the year, and A the final amount.

By replacing 0.0645 (6.45%) for r, 4 for n, 3 for t and 5500 for P into the above equation, we get:

$A=5500(1+\frac{0.0645}{4})^{4\times3}=6663.8978$

Then, after 3 years you will have $6663.9.

In order to determine the APY, we can use the following formula:

$APY=100\times((1+r/n)^n-1)$

Where n is the number of times the interest is compounded a year (4) and r is the rate of interest (0.0645), then we get:

$APY=100\times((1+0.0645\/4)^4-1)=6.61$

Then, the APY equals 6.61%