The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods.The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly.The first deposit will be made today.What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity to calculate the total amount saved over 5 years with monthly deposits of $1500:

FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
where
PMT = $1500 (monthly deposit)
r = 0.045 (annual interest rate)
n = 12 (number of compounding periods per year)
t = 5 (number of years)

FV = $102,948.13

To find the lump sum deposit that would yield the same future value after 5 years, we can use the formula for the present value of a lump sum:

PV = FV / (1 + r)^t

PV = $102,948.13 / (1 + 0.045)^5

PV = $80,760.79

Therefore, the answer is B. A lump sum deposit of $80,760.79 made today would yield the same savings as monthly deposits of $1500 for 5 years at 4.5% compounded monthly.

The Design Team Just Decided to Save $1,500 a Month