A friend of yours just bought a new sports car with a 4000 d

A friend of yours just bought a new sports car with a $4000 down payment, and her $26,000 car loan is financed at an interest rate of 0.50% per month for 48 months. After 2 years, the \"Blue Book\" value of her vehicle in the used-car marketplace is $12,000

a. How much does your friend still owe on the car loan immediately after she makes her 24th payment?

Solution

interest rate = 0.5% , time period = 48 months

PV = $26000

monthly payment = y

y/(1 + 0.5%) + ..... + y/(1 + 0.5%)⁴⁸ = 26000

y = $610.61

a)

Car loan owed (after 24th payment) = PV of remaining 24 monthly payments

Car loan owed (after 24th payment) = 610.61/(1 + 0.5%) + ...... +  610.61/(1 + 0.5%)²⁴

Car loan owed (after 24th payment) = $13777.13