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 5% compounded semiannually. Round to nearest dollar.
A) $18,950
B) $33,226
C) $18,589
D) $33,622
E) None of these

Question

Quizplus · Accepted Answer

To find out how much Mia needs to put in the bank today, we can use the formula for compound interest:

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

where A is the future amount, P is the present amount (what Mia needs to put in the bank today), r is the interest rate (5% in this case), n is the number of times the interest is compounded per year (semiannually, so n = 2), and t is the number of years.

Plugging in the values given, we get:

$25,000 = P(1 + 0.05/2)^(2*6)
$25,000 = P(1.025)^12
$25,000 = P(1.344)
P = $18,589 (rounded to the nearest dollar)

Therefore, Mia needs to put $18,589 in the bank today to have $25,000 six years from now, earning 5% compounded semiannually.

Mia Kaminsky Wants to Attend Riverside Community College