Question

1, How many years will it take to pay off a car loan of $25,703 at an annual rate of 12.38% compounded monthly if you make monthly payment of $614?

Please round your answer to the second decimal. e.g. 1.11

2.

You are saving money to travel around the globe. You've taken your first job and you plan to save $434 each month into the bank account that pays 7.37% compounded monthly for the next three years for your grad school fund. How much money will you accumulate by the end of year three?

Please round your answer to the second decimal without dollar sign. e.g. 1.11

Answer 1

Solution

1. Present value of annuity=Annuity amount*((1-(1/(1+r)^n))/r)

where

n=number of periods

r=rate of interest per period=12.38/12=1.031667%

Annuity amount=614

Present value of annuity=25703

Putting values in formula

25703=614*((1-(1/(1+.01031667)^n))/.01031667)

Solving we get n=55.08754 months=55.08754/12=4.59 years

Number of years taken to repay=4.59 years

2. Future value of annuity= Annuity amount*(((1+r)^n-1)/r)

n=number of periods=12*3=36

r=rate of interest per period=7.37/12=0.614167% per month

Annuity amount=434

Future value of annuity=434*(((1+.00614167)^36-1)/.00614167)

=17426.30

Amount accumulated after 3 years =17426.30

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