Question

Sarah wants to save $20,000 to use for a down payment on a home. She deposits some money into a 4-year certificate of deposit (CD) with an annual interest rate of 4.5% compounded monthly. How much does Sarah need to deposit in the CD to reach her goal of having $20,000 in 4 years? Round your final answer to the nearest dollar.

Hint: Use the formula PV=frac(S,sup((1+i),n)).


$12.583

$16,711

$4,785

$5,000

Answer 1

To reach Sarah's goal of having $20,000 in 4 years, we'll use the formula for the present value of a future sum (PV):

PV = FV / (1 + i)^n

Here, FV is the future value ($20,000), i is the interest rate per period (0.045/12), and n is the number of periods (4 years * 12 months/year).

PV = $20,000 / (1 + 0.045/12)^(4*12)

PV ≈ $16,711

So, Sarah needs to deposit approximately $16,711 into the 4-year CD to reach her goal of having $20,000 in 4 years. The answer is:

$16,711