Question

You have just purchased a car and taken out a $39,000 loan. The loan has a​ five-year term with monthly payments and an APR of 5.5% . 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

First of All calculate EMI.

The formula used for arriving at the EMI

EMI = [P * R * (1+R) ^n] / [(1+R)^ n-1]

Here, P= Principal loan amount, R= Rate of interest, n= Number of monthly instalments.
P = $39,000, R = 0.4583 Monthly Rate(5.5/12), N = 60 (12*5)

= [39000*0.4583* (1+0.4583)^60 / [(1+0.4583)^60-1]

EMI will be $744.95

(A)

During the First Month we pay below amount as a Interest and Principal.

Interest = Principal*Rate of Interest

Interest = $39,000 * 5.5% = $2145 For 12 Months

1 Month Interest = 2145/12 = $178.75

1 month principal = 744.95-178.75 = $566.20

Cosing balance of loan = $38,433.80

2 month $38,433.80*5.5% / 12 = $176.15

2 month principal = 744.95-176.15 = $568.79

Closing Balance = $37865.01

Simillarly interest will be calculated on closing balance for all the month

1 Year Interest = $1971.08

1 year principal = (744.95*12)-1971.08 = $6968.32

Closing Balance = $32031.74

(B)

Closing Balance at 3 year end = $16,893.85

4th Year Interest = $727.20

4th year principal = $8211.54

Closing Balance at 3 year end = $8678.63