Question

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?

Answer 1

Answer:

A deposit of 36,922.02 dollars will be equivalent to the series of emergencies deposits of 2,000 starting today.

Explanation:

we need to know the future value of the emergencies deposit and then, calculate which lump sum can generate the same amount. As the deposit are done at the beginning It will be an annuity-due:

$C \times \frac{(1+r)^{time} -1}{rate}(1+r) = FV$

C 2,000

time      36 (3 years x 12 months per year)

rate 0.045

$2000 \times \frac{(1+0.045)^{36} -1 }{0.045}(1+0.045) = FV$

FV $180,082.6885

Now we calculate the lump sum which yield this amount as well:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $180,082.6885

time   36.00

rate  0.045

$\frac{180082.68854409}{(1 + 0.045)^{36} } = PV$  

PV   36,922.02