Question

You currently have two loans outstanding: a car loan and a student loan. The car loan requires that you pay $313 per month, starting next month for 35 more months. Your student loan is requires that you pay $133 per month, starting next month for the next 115 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 $451 per month for the next 45 months, starting

next month. If your investments earn 4.21% 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

Present Value of Car loan

P = monthly payment = $313

n = 35 months

r = monthly interest rate = 4.21%/12 = 0.3508333333%

Present Value of car loan = P * [1 - (1+r)^-n] / r

= $313 * [1 - (1+0.3508333333%)^-35] / 0.3508333333%

= $313 * 0.11536191 / 0.003508333333

= $10,292.1457

= $10,292.15

Present Value of Student loan

P = monthly payment = $133

n = 115 months

r = monthly interest rate = 4.21%/12 = 0.3508333333%

Present Value of student loan = P * [1 - (1+r)^-n] / r

= $133 * [1 - (1+0.3508333333%)^-115] / 0.3508333333%

= $133 * 0.331522051 / 0.003508333333

= $12,567.9143

= $12,567.91

Present Value of debt consolidation company loan

P = monthly payment = $451

n = 45 months

r = monthly interest rate = 4.21%/12 = 0.3508333333%

Present Value of student loan = P * [1 - (1+r)^-n] / r

= $451 * [1 - (1+0.3508333333%)^-45] / 0.3508333333%

= $451 * 0.145807378 / 0.003508333333

= $18,743.6943

= $18,743.69

Amount saved / loss after taking debt consolidation company offer = Present Value of Car loan + Present Value of Student Loan - Present Value of Debt consolidation company loan

= $10,292.15 + $12,567.91 - $18,743.69

= $4,116.37

Therefore, amount saved on accepting the offer is $4,116.37