Problem 5.25 Samantha plans to invest some money so that she has $4,800 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 $.

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TomShelby TomShelby · Answer 1 · 2019-09-05T23:11:06+02:00

Answer:

A 4,231.78

B 4,145.05

C 4,110.81

D 4,099.39

Explanation:

We have to calculate with compounding interest the present value of the 4,800 to know how much do we need to invest for each case.

[tex]Amount \div (1+ \frac{r}{n} )^{time* n} = Principal[/tex]

Amount = 4,800

First case:

rate = 0.042

compounding daily

[tex]4,800\div (1+ \frac{0.042}{365} )^{3* 365} = Principal[/tex]

Principal = 4231.78194

Second case:

rate = 0.049

compounding monthly

[tex]Amount \div (1+ \frac{0.049}{12} )^{3* 12} = Principal[/tex]

Principal = 4145.051563

Third case:

rate = 0.052

compounding quarterly

[tex]Amount \div (1+ \frac{0.052}{4} )^{3* 4} = Principal[/tex]

Principal = 4110.814626

Fourth case:

rate = 0.054

compounding annually

[tex]Amount \div (1+ \frac{0.054}{1} )^{3* 1} = Principal[/tex]

Principal = 4099.39158