Question

You currently have two loans outstanding: a car loan and a student loan. The car loan requires that you pay $316 per month, starting next month for 26 more months. Your student loan is requires that you pay $103 per month, starting next month for the next 69 months. A debt consolidation company gives you the following offer: It will pay off the balances of your two loans today and then charge you $475 per month for the next 43 months, starting next month. If your investments earn 4.88% APR, compounded monthly, how much would you save or lose by taking the debt consolidation company’s offer? If you lose, state your answer with a negative sign (e.g., -25,126)

Answer 1

Gain or loss= (PV of Car loan+PV of Student loan)-PV of debt consolidation company

PV=Mothly Installment amount*PVAF@ r rate for n periods

PVAF=[(1+r)^{^n}-1] / [(1+r)^{^n}*r]

where r (monthly)=4.88/12.4067% or .004067

PVAF of Car loan installments =[(1+.004067)^{^26}-1] / [(1+.004067)^{^26}*.004067]

=24.6251

PVAF of Student loan installments =[(1+.004067)^{^69}-1] / [(1+.004067)^{^69}*.004067]

=60.0583

PVAF of Debt consolidation company installments =[(1+.004067)^{^69}-1] / [(1+.004067)^{^69}*.004067]

=60.0583

PV of car loan=7781.53 (i.e.316*24.6251)

PV of student loan=6186 (i.e.103*60.0583)

PV of debt consolidation loan=18703.98 (i.e.475*39.3768)

Gain or loss= (7781.53+6186)-18703.98

=-4736.45

Hence he will lose by taking the debt consolidation company's offer.