Question

Maryann is planning a wedding anniversary gift of a trip to Hawaii for her husband at the end of 5 years. She will have enough to pay for the trip if she invests $5,000 per year until that anniversary and plans to make her first $5,000 investment on their first anniversary. Assume her investment earns a 4 percent interest rate, how much will she have saved for their trip if the interest is compounded in each of the following ways?

a. Annually        b.            Quarterly             c.            Monthly

Answer 1

- maryann will invests $5000 at the end of each year for 5 years

Calculating the Future values at the end of year 5 in the following scenarios:-

a), Interest rate compounded annually.

Where, C= Periodic Payments = $5000

r = Periodic Interest rate = 4%

n= no of periods = 5 years

Future Value = $27,081.61

So, the amount she have saved for their trip is $27,081.61

b). Interest rate compounded Quarterly.

First, we will Calculate the Effective Annual Interest rate:-

Where,

r = Interest rate = 4%

m = no of times compounding in a year = 4 (compounded quarterly)

EAR = 1.040604-1

EAR = 4.0604%

Now, calculating Future Value:-

Where, C= Periodic Payments = $5000

r = Periodic Interest rate = 4.0604%

n= no of periods = 5 years

Future Value = $27,114.32

So, the amount she have saved for their trip is $27,114.32

c). Interest rate compounded monthly.

First, we will Calculate the Effective Annual Interest rate:-

Where,

r = Interest rate = 4%

m = no of times compounding in a year = 12 (compounded monthly)

EAR = 1.0407415-1

EAR = 4.07415%

Now, calculating Future Value:-

Where, C= Periodic Payments = $5000

r = Periodic Interest rate = 4.07415%

n= no of periods = 5 years

Future Value = $27,121.77

So, the amount she have saved for their trip is $27,121.77