Question

(Future value)  Leslie​ Mosallam, who recently sold her​ Porsche, placed ​$10200 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 8 percent or one that pays 10 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? a.  After placing ​$10200 in a savings account paying annual compound interest of 6 percent​, the amount of money that will accumulate if Leslie leaves the money in the bank for 3 ​year(s) is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

a.

1. 6% - 3 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.06)^3

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.191016

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $12148.36

2. 6% - 7 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.06)^7

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.50363

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $15337.03

3. 6% - 17 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.06)^17

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 2.69277

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $27466.28

Rework part ​(a​) using 8 percent and 10 percent

1. 8% - 3 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.08)^3

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.25971

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $12849.06

2. 8% - 7 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.08)^7

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.71382

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $17481.01

3. 8% - 17 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.08)^17

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 3.7000

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $37740.18

4. 10% - 3 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.10)^3

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.331

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $13576.20

5. 10% - 7 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.10)^7

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 1.94817

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $19876.91

6. 10% - 17 Years

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = Amount * (1 + r)^n

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * (1 + 0.10)^17

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = 10200 * 5.05447

Amount of money that will accumulate if Leslie leaves the money in the bank for 3 Years = $51555.60

c. the conclusions are

when interest rates increase keeping time constant, the future sum will increase

when time increase keeping interest rate constant, the future sum will increase

Interest Rate and Time are directly proportional to Future Sum