Question

Mark wants to buy a new car for his wife and agrees with a 1.5-year, $12,000loan. The financial institution quotes this loan at 10.5%, compounded monthly. Sixmonths later, Mark is offered an optional loan from another financial institution. The newloan is quoted at 9.25% and Mark asks that the number of payments be set to 12. A 1%fee will be added to the remaining loan balance for the principal of the new loan.

What was the first loan monthly payment and what is the amount Mark is going to pay for thenew one? Is it a good idea to change?

Answer 1

1. PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

12000= A*(1-1/(1+10.5%/12)^18)/(10.5%/12)

12000= A*16.58717111

A=12000/16.58717111= 723.450667

Monthly payment= $723.45

1. Amount outstanding after 6 payments (12 remaining)=Annuity*(1-1/(1+rate)^number of terms)/rate

= 723.450667*(1-1/(1+10.5%/12)^12/(10.5%/12)

=8207.171109

Principal of the new loan= 8207.171109*101%

= 8289.24282

New monthly payments:

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

8289.24282= A*(1-1/(1+9.25%/12)^12)/ (9.25%/12)

8289.24282= A*11.4197682

A= 725.8678703

This is not a good arrangement because Mark has to pay higher amount per month for 12 months.