The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years?

Question

Quizplus · Accepted Answer

To find out the monthly deposit amount, we can use the formula for compound interest:

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

where A is the amount after t years, P is the principal (in this case, the monthly deposit), r is the annual interest rate (4.5%), n is the number of times the interest is compounded per year (12 for monthly), and t is the time in years.

We want to find out the monthly deposit amount that will yield the same amount as a lump sum deposit after 3 years, so we need to solve for P:

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

First, let's find out how much the monthly deposits will accumulate to after 3 years:

n = 12, r = 0.045/12, t = 3*12
A = 2000 * ((1 + 0.045/12)^(12*3) - 1) / (0.045/12)
A = $76,842.70

Now we can use this amount to find the lump sum deposit that would yield the same result:

n = 12, r = 0.045/12, t = 3
P = 76842.70 / ((1 + 0.045/12)^(12*3))
P = $67,485.97

Therefore, the answer is B.

The Distribution Point Plans to Save $2,000 a Month for the Next