John bought his new pickup for no money down with with an amortized lo
QUESTION
John bought his new pickup for no money down with with an amortized loan at 2.5%. For a term of 48 months, his monthly payment is 523.18$. How much will he still owe after 3 years?
*This answer assumes that 2.5% is the yearly rate of interest. If it is the monthly rate of interest, all (0.025/12) should be changed to (0.025) STEP 1. First we need to figure out the present value of the loan itself (how much is being borrowed). We do this either in the financial calculator or using the formula for the present value of an annuity; PMT [(1 (1 / (1 i)^n)) / i] or 523.18 * [(1 (1 / (1 (0.025/12))^(48))) / (0.025/12)] = 23,874.20 In the financial calculator, it is done as such; FV=0 PMT=523.18 N=48 I=2.5/12 calculate PV STEP 2. We now can calculate the future value of the loan after 3 years, using the future value of a single sum and the future value of an annuity, and subtracting the two. Essentially (Sum of obligation in year 3 minus sum of payments by year 3) Future value of an annuity = PMT [((1 i)^n 1) / i] =523.18*(((1 0.025/12)^(36)-1)/(0.025/12)) =
,537.65 Future Value of a single sum = PV*(1 i)^n =23,874.20*(1 0.025/12)^36 = 25,731.61 Now we subtract the two for our answer; 25,731.61 19,537.65 = 6,193.96 OR in the financial calculator, we can do both at once; PV = -23,874.20 N = 36 I = 2.5/12 PMT = 523.18 calculate FV Note that some calculators require the interest rate to be put in differently, and note negative signs where necessary. Mainly, negative signs need to be used when one value is a cash inflow and another is a cash outflow. We assume borrowing is an inflow for the borrower, and making payments is an outflow. Good luck!
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