Please show detailed work. Thank You. (Related to Checkpoint 5.2)(Future value)L
ID: 2815428 • Letter: P
Question
Please show detailed work. Thank You.
(Related to Checkpoint 5.2)(Future value)Leslie Mosallam, who recently sold her Porsche, placed $9,800 in a savings account paying annual compound interest of 4 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 6 percent or one that pays 8 percent. Rework part (a) using 6 percent and 8percent.
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 $9 comma 800in a savings account paying annual compound interest of 4 percent, the amount of money that will accumulate if Leslie leaves the money in the bank for 2 year(s) is ___ (round to the nearest cent.)
Explanation / Answer
We have
Future Value = Present value * (1+ rate per period)^no. of periods
a. Calculation of money that will accumulate if Leslie leaves the money in the bank for 2, 6, and 16 year(s).
- 2 years
Future Value = 9800 * (1.04)^2
= 9800 * 1.0816
= 10599.68
- 6 years
Future Value = 9800 * (1.04)^6
= 9800 * 1.265319
= 12400.13
- 16 years
Future Value = 9800 * (1.04)^16
= 9800 * 1.872982
= 18355.22
b. Rework a if interest rates are 6% and 8%
1) 6%
2 years
Future Value = 9800 * (1.06)^2
= 9800 * 1.1236
= 11011.28
- 6 years
Future Value = 9800 * (1.06)^6
= 9800 * 1.418519
= 13901.49
- 16 years
Future Value = 9800 * (1.06)^16
= 9800 * 2.540352
= 24895.45
2) 8%
2 years
Future Value = 9800 * (1.08)^2
= 9800 * 1.1664
= 11430.72
- 6 years
Future Value = 9800 * (1.08)^6
= 9800 * 1.586874
= 15551.37
- 16 years
Future Value = 9800 * (1.08)^16
= 9800 * 3.425943
= 33574.24
c. What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you just did?
As youy know
Future Value = Present value * (1+ rate per period)^no. of periods
THerefore there is a direct relationship between interest rates, time, and future sums. When we look at the above example, you can see that as the time increases future sums also increases. Also as when interest rates increases future sums also increases.
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