Question

Samantha plans to invest some money so that she has $4,700 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. Amount required to be invested $ b. 4.9 percent compounded monthly. Amount required to be invested $ c. 5.2 percent compounded quarterly. Amount required to be invested $ d. 5.4 percent compounded annually. Amount required to be invested $

Answer 1

Present value is computed as shown below:

= Future value / (1 + r)ⁿ

a. The amount is computed as shown below:

= $ 4,700 / (1 + 0.042 / 365) ^{365 x 3}

= $ 4,143.62 Approximately

b. The amount is computed as shown below:

= $ 4,700 / (1 + 0.049 / 12) ^{12 x 3}

= $ 4,058.70 Approximately

c. The amount is computed as shown below:

= $ 4,700 / (1 + 0.052 / 4) ^{4 x 3}

= $ 4,025.17 Approximately

d. The amount is computed as shown below:

= $ 4,700 / 1.054³

= $ 4,013.99 Approximately

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