amantha plans to invest some money so that she has $2,700 at the end of three ye
ID: 1175503 • Letter: A
Question
amantha plans to invest some money so that she has $2,700 at the end of three years. How much should she invest today given the following choices? (Use 365 days for calculation. If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your final answer to the nearest penny.)
a. 4.2 percent compounded daily.
b. 4.9 percent compounded monthly.
c. 5.2 percent compounded quarterly.
d. 5.4 percent compounded annually.
Amount required t
Explanation / Answer
a,.Daily Compounding = Amount = Principal ( 1 + Rate / 365 ) ^365 x Time
Daily Compounding = 2700 = X ( 1 + 0.042 / 365 ) ^365 x 3
Daily Compounding = 2700 = X (1.1342739)
Daily Compounding = X = 2700 / 1.1342739 = $2380.38
b.Monthly Compounding = Amount = Principal ( 1 + Rate / 12 ) ^12 x Time
Monthly Compounding = 2700 = X ( 1 + 0.049 / 12 ) ^12 x 3
Monthly Compounding = 2700 = X (1.1580073)
Monthly Compounding = X = 2700 / 1.1580073 = $2331.59
c.Quarterly Compounding = Amount = Principal ( 1 + Rate / 4 ) ^4 x Time
Quarterly Compounding = 2700 = X ( 1 + 0.052 / 4 ) ^4 x 3
Quarterly Compounding = 2700 = X (1.16765177)
Quarterly Compounding = X = 2700 / 1.16765177 = $2312.33
d.Annual Compounding = Amount = Principal ( 1 + Rate ) ^1 x Time
Annual Compounding = 2700 = X ( 1 + 0.054 ) ^1 x 3
Annual Compounding = 2700 = X (1.170905464)
Annual Compounding = X = 2700 / 1.170905464 = $2305.91
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