Question

You have just taken out a $26,000 car loan with a 7 % APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

When you make your first​ payment,​$__ will go toward the principal of the loan and ​$__ will go toward the interest.  ​(Round to the nearest​ cent.)

Answer 1

Step 1: Calculate Amount of Monthly Payment

The amount of monthly payment can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value (if any).

Rate = 7%/12, Nper = 5*12 = 60, PV = $26,000 and FV = 0 [we use 12 since the compounding is monthly]

Using these values in the above formula/function for PMT, we get,

Monthly Payment = PMT(7%/12,60,26000,0) = $514.831162

______

Step 2: Calculate Amount that will Go Toward Principal and Interest in First Payment

The amount that will go toward principal and interest in the first payment is derived as below:

Interest in First Month Payment = Loan Amount*Interest Rate/12 = 26,000*7%/12 = $151.666667or $151.67 (when rounded to the nearest cent)

Principal in First Month Payment = Amount of Monthly Payment from Step 1 - Interest in First Month Payment = 514.831162 - 151.666667 = $363.164495 or $363.16 (when rounded to the nearest cent)

When you make your first​ payment,​ $363.16 will go toward the principal of the loan and $151.67 will go toward the interest.