Celesta Frank wants to go on a cruise in three years. She could earn 8 percent compounded daily in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)
A) $6,432
B) $7,826
C) $8,148
D) $7,763

Question

Quizplus · Accepted Answer

To find the initial deposit, we can use the formula for compound interest:

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

where A is the final amount, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times compounded per year, and t is the time in years.

In this case, we want to solve for P:

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

Plugging in the given values, we get:

P = 10000/(1 + 0.08/365)^(365*3)
P = $8,147.62

Rounding to the nearest dollar, the answer is $8,148, so the best choice is C.

Celesta Frank Wants to Go on a Cruise in Three