5.22 Multiple compounding periods: Samantha is looking to invest some money, so

Question

5.22 Multiple compounding periods: Samantha is looking to invest some money, so she can collect $5,500 at the end of three years. How much should she invest today? a. 4.2 percent compounded daily b. 4.9 percent compounded monthly c. 5.2 percent compounded quarterly d. 5.4 percent compounded annually 5.22 Multiple compounding periods: Samantha is looking to invest some money, so she can collect $5,500 at the end of three years. How much should she invest today? a. 4.2 percent compounded daily b. 4.9 percent compounded monthly c. 5.2 percent compounded quarterly d. 5.4 percent compounded annually

Explanation / Answer

Answer to Part a:

Future Value = $5,500
Time = 3 years
or Time (n) = 3 years * 365 = 1,095 days
Rate = 4.2% p.a.
or Rate (r) = 0.0115% per day

Future Value = Present Value * (1 + r)^ n
$5,500 = Present Value * (1 + 0.000115)^ 1,095
$5,500 = Present Value * (1.000115)^ 1,095
$5,500 = Present Value * 1.1343
Present Value = $4,848.81

Samantha should invest $4,848.81 today to collect $5,500 at the end of 3 years.

Answer to Part b:

Future Value = $5,500
Time = 3 years
or Time (n) = 3 years * 12 = 36 months
Rate = 4.9% p.a.
or Rate (r) = 0.4083% per month

Future Value = Present Value * (1 + r)^ n
$5,500 = Present Value * (1 + 0.004083)^ 36
$5,500 = Present Value * (1.004083)^ 36
$5,500 = Present Value * 1.1580
Present Value = $4,749.57

Samantha should invest $4,749.57 today to collect $5,500 at the end of 3 years.

Answer to Part c:

Future Value = $5,500
Time = 3 years
or Time (n) = 3 years * 4 = 12 Quarters
Rate = 5.2% p.a.
or Rate (r) = 1.30% per Quarter

Future Value = Present Value * (1 + r)^ n
$5,500 = Present Value * (1 + 0.013)^ 12
$5,500 = Present Value * (1.013)^ 12
$5,500 = Present Value * 1.1677
Present Value = $4,710.11

Samantha should invest $4,710.11 today to collect $5,500 at the end of 3 years.

Answer to Part d:

Future Value = $5,500
Time (n) = 3 years
Rate (r)= 5.4% p.a.

Future Value = Present Value * (1 + r)^ n
$5,500 = Present Value * (1 + 0.054)^ 3
$5,500 = Present Value * (1.054)^ 3
$5,500 = Present Value * 1.1709
Present Value = $4,697.24

Samantha should invest $4,697.24 today to collect $5,500 at the end of 3 years.

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