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(Future value) Leslie Mosallam, who recently sold her Porsche, placed $10, 000 in a savings account...

(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 $

Expert Solution

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.

jeff jeffy answered 1 year ago

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