Question

 ​(Future value)  Leslie​ Mosallam, who recently sold her​ Porsche, placed ​$8400 in a savings account paying annual compound interest of 5 percent.

a.  Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for 2​, 6​, and 16 ​year(s).

b.  Suppose Leslie moves her money into an account that pays 7 percent or one that pays 9 percent. Rework part ​(a​) using 7 percent and 9 percent.

c.  What conclusions can you draw about the relationship between interest​ rates, time, and future sums from the calculations you just​ did?

Answer 1

a.

Interest Rate = 5 percent per year

Initial deposit = $8,400

For 2 years,

Accumulated Value = 8400(1+0.05)²

Accumulated Value = $9,261

For 6 years,

Accumulated Value = 8400(1+0.05)⁶

Accumulated Value = $11,256

For 16 years,

Accumulated Value = 8400(1+0.05)¹⁶

Accumulated Value = $18,336.14

b.

Interest Rate = 7%

For 2 years,

Accumulated Value = 8400(1+0.07)²

Accumulated Value = $9,617.16

For 6 years,

Accumulated Value = 8400(1+0.07)⁶

Accumulated Value = $12,606.13

For 16 years,

Accumulated Value = 8400(1+0.07)¹⁶

Accumulated Value = $24,798.17

Interest Rate = 9%

For 2 years,

Accumulated Value = 8400(1+0.09)²

Accumulated Value = $9,980.04

For 6 years,

Accumulated Value = 8400(1+0.09)⁶

Accumulated Value = $14,087.64

For 16 years,

Accumulated Value = 8400(1+0.09)¹⁶

Accumulated Value = $33,350.57

c.

Value of Future Value of Investment is directly proportional to the number of years and interest rate,

FV = PV(1 + r)^t