Question

You have just purchased a car and taken out a $35,000 loan. The loan has a​ five-year term with monthly payments and an APR of 6.1%.

a. How much will you pay in​ interest, and how much will you pay in​ principal, during the first​ month, second​ month, and first​ year? (Hint: Compute the loan balance after one​ month, two​ months, and one​ year.)

b. How much will you pay in​ interest, and how much will you pay in​ principal, during the fourth year​ (i.e., between three and four years from​ now)? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Answer (a):

First let us calculate the monthly payments:

Loan Amount = $35,000

Month Interest = APR / 12 = 6.1% / 12

Duration = 5 years = 5 * 12 = 60 months

To get monthly payment we will use PMT function:

= PMT (rate, nper, pv, fv, type)

= PMT (6.1%/12, 60, -35000, 0, 0)

= $678.276704

Monthly payment = $678.28

First Month:

Interest paid = 35000 * 6.1%/12 = $177.92

Principal paid = 678.28 - 177.92 = $500.36

Second Month:

Interest paid = (35000 - 500.36) * 6.1%/12 = $175.37

Principal paid = 678.28 - 175.37 = $502.90

One Year:

On completion of one year monthly installments paid = 12

Remaining monthly installments = 60 - 12 = 48

Loan outstanding at the end of one year = Present value of remaining 48 monthly payments

= PV (rate, nper, pmt, fv, type)

= PV (6.1%/12, 48, -678.276704, 0, 0)

= $28824.93

Hence:

During first year Principal paid = 35000 - 28824.93 =$6175.07

During first one interest paid = Monthly payments * 12 - Principal paid = 678.276704 * 12 - 6175.07 = $1964.25

Answer (b):

To calculate interest, and principal repaid during the fourth year, we have to calculate loan balance at the end of year 3 and loan balance at the end year 4.

Loan outstanding at the end of Year 3 = Present value of remaining 24 monthly payments

= PV (rate, nper, pmt, fv, type)

= PV (6.1%/12, 24, -678.276704, 0, 0)

= $15288.318580

Loan outstanding at the end of Year 4 = Present value of remaining 12 monthly payments

= PV (rate, nper, pmt, fv, type)

= PV (6.1%/12, 12, -678.276704, 0, 0)

= $7876.643847

Hence:

Principal repaid during year 4 = 15288.318580 - 7876.643847 = $7,411.67

Interest paid during Year 4 = Monthly payments * 12 - Principal paid = 678.276704 * 12 - 7411.67 = $727.65

Principal repaid during year 4 = $7,411.67

Interest paid during Year 4 = $727.65