Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly 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 out how much Celesta needs to deposit today to have $10,000 in three years at an 8.2% annual interest rate compounded monthly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value (amount she needs to deposit today), $FV$ is the future value ($10,000), $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of compounding periods (months in 3 years).Given:- $FV = $10,000$- Annual interest rate = 8.2% or 0.082- Monthly interest rate $r = \frac{0.082}{12}$- Number of years = 3, so number of months $n = 3 \times 12 = 36$Plugging these values into the formula:$$PV = \frac{10,000}{(1 + \frac{0.082}{12})^{36}}$$$$PV = \frac{10,000}{(1 + 0.006833)^{36}}$$$$PV = \frac{10,000}{(1.006833)^{36}}$$$$PV = \frac{10,000}{1.276281}$$$$PV ≈ 7,826$$Therefore, Celesta needs to deposit approximately $7,826 today to have $10,000 in three years, given the conditions.

Celesta Frank Wants to Go on a Cruise in Three