Question

Helen plans to invest some money so that she has $3,900 at the end of three years. Determine how much should she invest today given the following choices: (Do not round intermediate calculations and 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

a

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+4.2/(365*100))^365-1)*100

Effective Annual Rate% = 4.2892

Future value = present value*(1+ rate)^time

3900 = Present value*(1+0.042892)^3

Present value = 3438.32

b

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+4.9/(12*100))^12-1)*100

Effective Annual Rate% = 5.0116

Future value = present value*(1+ rate)^time

3900 = Present value*(1+0.050116)^3

Present value = 3367.85

c

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+5.2/(4*100))^4-1)*100

Effective Annual Rate% = 5.3023

Future value = present value*(1+ rate)^time

3900 = Present value*(1+0.053023)^3

Present value = 3340.04

d

Future value = present value*(1+ rate)^time

3900 = Present value*(1+0.054)^3

Present value = 3330.76