You have just purchased a car and taken out a $47,000 loan The loan has a five-y
ID: 1176112 • Letter: Y
Question
You have just purchased a car and taken out a $47,000 loan The loan has a five-year term with monthly payments and an APR of 5.9%, 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) 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) During the first month, you will pay sin principal (Round to the nearest cent) During the first month, you will pay Sin interest (Round to the nearest cent) During the second month, you will pay Sin principal. (Round to the nearest cent.) During the second month, you will pay in interest (Round to the nearest cent) During the frst year, you will pay sin principal (Round to the nearest cent) During the first year, you will pay in interest. (Round to the nearest cent) b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (de between three and four years from now)? During the fourth year you will pay sin principal (Round to the nearest cent) During the fourth year, you will pay sin interest. (Round to the nearest cent )Explanation / Answer
Amount Borrowed = $47,000
Annual Interest Rate = 5.90%
Monthly Interest Rate = 0.4917%
Period = 5 years or 60 months
Monthly Payment * PVIFA(0.4917%, 60) = $47,000
Monthly Payment * (1 - (1/1.004917)^60) / 0.004917 = $47,000
Monthly Payment * 51.84968 = $47,000
Monthly Payment = $906.47
Answer a.
During 1st month:
Interest paid = $47,000 * 0.4917%
Interest paid = $231.10
Principal paid = $906.47 - $231.10
Principal paid = $675.37
Loan outstanding = $47,000 - $675.37
Loan outstanding = $46,324.63
During 2nd month:
Interest paid = $46,324.63 * 0.4917%
Interest paid = $227.78
Principal paid = $906.47 - $227.78
Principal paid = $678.69
During 1st year:
Total Amount paid = 12 * $906.47
Total Amount paid = $10,877.64
Loan outstanding after 1st year = $906.47 * PVIFA(0.4917%, 48)
Loan outstanding after 1st year = $906.47 * (1 - (1/1.004917)^48) / 0.004917
Loan outstanding after 1st year = $906.47 * 42.66322
Loan outstanding after 1st year = $38,672.93
Principal Paid = $47,000 - $38,672.93
Principal Paid = $8,327.07
Interest Paid = $10,877.64 - $8,327.07
Interest Paid = $2,550.57
Answer b.
During 4th year:
Total Amount paid = 12 * $906.47
Total Amount paid = $10,877.64
Loan outstanding after 3rd year = $906.47 * PVIFA(0.4917%, 24)
Loan outstanding after 3rd year = $906.47 * (1 - (1/1.004917)^24) / 0.004917
Loan outstanding after 3rd year = $906.47 * 22.58573
Loan outstanding after 3rd year = $20,473.29
Loan outstanding after 4th year = $906.47 * PVIFA(0.4917%, 12)
Loan outstanding after 4th year = $906.47 * (1 - (1/1.004917)^12) / 0.004917
Loan outstanding after 4th year = $906.47 * 11.62511
Loan outstanding after 4th year = $10,537.81
Principal Paid = $20,473.29 - $10,537.81
Principal Paid = $9,935.48
Interest Paid = $10,877.64 - $9,935.48
Interest Paid = $942.16
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