Mia Kaminsky wants to attend Riverside Community College. She will need to have $25,000 six years from today. Mia is wondering what she will have to put in the bank today so that she will have $25,000 six years from now. Her bank pays 6% compounded semiannually. Using the tables in the handbook, the amount Mia will have to deposit is:
A)$18,950
B)$17,625
C)$17,535
D)$33,622
E)None of these

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we have:

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

where A is the amount after t years, P is the principal (amount deposited), r is the annual interest rate (6%), n is the number of times the interest is compounded per year (2, since it is compounded semiannually), and t is the number of years (6).

We want to solve for P, so we rearrange the formula:

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

Substituting the given values, we have:

P = $25,000/(1 + 0.06/2)^(2*6) = $17,535.10

Therefore, Mia will have to deposit $17,535.10 today to have $25,000 six years from now. The answer is C.

Mia Kaminsky Wants to Attend Riverside Community College