Howard is saving for a long holiday.He deposits a fixed amount every month in a bank account with an EAR of 7.5%.If this account pays interest every month then how much should he save from each monthly paycheck in order to have $10,000 in the account in two years' time?
A)$161
B)$166
C)$388
D)$4818

Question

Quizplus · Accepted Answer

Using the formula for future value of an annuity:

FV = PMT * [(1 + r/n)^(nt) - 1] / (r/n)

where
FV = future value
PMT = monthly payment
r = annual interest rate
n = number of times interest is compounded per year
t = number of years

We can solve for PMT:

PMT = FV * (r/n) / [(1 + r/n)^(nt) - 1]

Plugging in the given values:

FV = $10,000
r = 7.5%
n = 12 (since interest is compounded monthly)
t = 2 years

PMT = $10,000 * (0.075/12) / [(1 + 0.075/12)^(12*2) - 1]
PMT = $387.83

Therefore, Howard should save $388 from each monthly paycheck in order to have $10,000 in the account in two years' time. The closest answer choice is C.

Howard Is Saving for a Long Holiday