Question

(Future value)  Leslie​ Mosallam, who recently sold her​ Porsche, placed ​$10, 000 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? a.After placing ​$10, 000 in a savings account paying annual compound interest of 5 percent​, the amount of money that will accumulate if Leslie leaves the money in the bank for 2 ​year(s) is ​$

Answer 1

1)

Future value after 2 years = Present value (1 + r)ⁿ

Future value after 2 years = 10,00 (1 + 0.05)²

Future value after 2 years = 10,00 * 1.1025

Future value after 2 years = 11,025.00

Future value after 6 years = Present value (1 + r)ⁿ

Future value after 6 years = 10,000 (1 + 0.05)⁶

Future value after 6 years = 10,000 * 1.3400956

Future value after 6 years = 13,400.96

Future value after 16 years = Present value (1 + r)ⁿ

Future value after 16 years = 10,000 (1 + 0.05)¹⁶

Future value after 16 years = 10,000 * 2.1828746

Future value after 16 years = 21,828.75

2)

7 percent:

Future value after 2 years = Present value (1 + r)ⁿ

Future value after 2 years = 10,000 + 0.07)²

Future value after 2 years = 10,000 * 1.1449

Future value after 2 years = 11,449.00

Future value after 6 years = Present value (1 + r)ⁿ

Future value after 6 years = 10,000 (1 + 0.07)⁶

Future value after 6 years = 10,000 * 1.5007304

Future value after 6 years = 15,007.30

Future value after 16 years = Present value (1 + r)ⁿ

Future value after 16 years = 10,000 (1 + 0.07)¹⁶

Future value after 16 years = 10,000 * 2.9521637

Future value after 16 years = 29,521.64

9 percent:

Future value after 2 years = Present value (1 + r)ⁿ

Future value after 2 years = 10,000 (1 + 0.09)²

Future value after 2 years = 10,000 * 1.1881

Future value after 2 years = 11,881.00

Future value after 6 years = Present value (1 + r)ⁿ

Future value after 6 years = 10,000 (1 + 0.09)⁶

Future value after 6 years = 10,000 * 1.6771

Future value after 6 years = 16,771.00

Future value after 16 years = Present value (1 + r)ⁿ

Future value after 16 years = 10,000 (1 + 0.09)¹⁶

Future value after 16 years = 10,000 * 3.9703059

Future value after 16 years = 39,703.06

There is a direct relationship between future value and time & interest rate. As time and interest rate increases, future value also increases.