Question

You want to get a car loan, you know you can afford to pay $200 a month for 36 months. If the bank offers you a yearly interest rate of 6%, which is compounded monthly, how much can you afford to borrow?

Please show the work and explain why this is a uniform series sinking fund example. Thanks!

Answer 1

Uniform monthly payment = $200

Time = 36 months

Monthly rate = 6%/12 = .5%

Let, amount to be borrowed = P

Then,

P = 200*(1-1/(1+.5%)^36)/.5%

P = $6574.20 or $6574

So, amount afforded to be borrowed is $6574.20 or $6574.

It is a uniform sinking fund example, because it is used to identify the amount of debt that can be repaid using a uniform monthly series of $200 over a period of time. Here, time period is 36 month, used to assess the level of debt to be paid. Hence, it is the case of uniform sinking fund.