Question

(Future value) Leslie​ Mosallam, who recently sold her​ Porsche, placed ​$8400 in a savings account paying annual compound interest of 6 percent.
a.  Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for 3​, 7​, and 17 ​year(s).
b.  Suppose Leslie moves her money into an account that pays 10 percent or one that pays percent. Rework part ​(a​) using 8 percent and 10 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

Answer : (a.) Calculation of Future Value :

Future Value = Present Value * (1 + rate)^number of period

Calculation of Future Value at 6% for 3 years

Future Value = 8400 * (1 + 0.06)^3

= 8400 * 1.191016

= 10004.53

Calculation of Future Value at 6% for 7 years

Future Value = 8400 * (1 + 0.06)^7

= 8400 * 1.50363

= 12630.49

Calculation of Future Value at 6% for 17 years

Future Value = 8400 * (1 + 0.06)^17

= 8400 * 2.692773

= 22619.29

(b.) Using 8 % as interest rate

Future Value = Present Value * (1 + rate)^number of period

Calculation of Future Value at 8% for 3 years

Future Value = 8400 * (1 + 0.08)^3

= 8400 * 1.259712

= 10581.58

Calculation of Future Value at 8% for 7 years

Future Value = 8400 * (1 + 0.08)^7

= 8400 * 1.713824

= 14396.12

Calculation of Future Value at 8% for 17 years

Future Value = 8400 * (1 + 0.08)^17

= 8400 * 3.700018

= 31080.15

Using 10%

Calculation of Future Value at 10% for 3 years

Future Value = 8400 * (1 + 0.10)^3

= 8400 * 1.331

=11180.4

Calculation of Future Value at 10% for 7 years

Future Value = 8400 * (1 + 0.10)^7

= 8400 * 1.948717

= 16369.22

Calculation of Future Value at 10% for 17 years

Future Value = 8400 * (1 + 0.10)^17

= 8400 * 5.05447

= 42457.55

(c.) There is positive relatioship between interst rate and future value because as the interest rate increases future value increases and vice-versa.

There is positive relatioship between time and future value because as the time increases future value increases and vice-versa.