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Exam 13: Loan Amortization; Mortgages

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Question 81

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A $125,000 loan at 6.0% compounded semi-annually will be repaid by monthly payments over a 20-year amortization period. a) Calculate the interest component of Payment 188. b) Calculate the principal component of Payment 101. c) Calculate the reduction of principal in Year 1. d) Calculate the reduction of principal in Year 20.

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a) $204.57; b) $446....

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Question 82

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Jakob borrowed $27,000 for a car. He is making monthly payments of $494.81 at 3.8% compounded monthly. Construct a partial amortization schedule showing details of the first two payments, payments 33 and 34, and the last two payments.

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Question 83

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A $100,000 mortgage at 7.3% compounded semi-annually with a 25-year amortization requires monthly payments. The mortgage allows the borrower to miss a payment once each year. How much will the amortization period be lengthened if the borrower misses the 12^th payment? (The interest that accrues during the 12^th month is converted to principal at the end of the 12^th month.)

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much interest will the borrower pay during the 4^th year?

How much interest is included in the third payment?

Larissa bought a stereo for $5,000. She made a down payment of $1,000, and financed the balance with monthly payments over four years at 8.5% compounded quarterly. Construct a partial amortization schedule showing details of the first two payments, payments 22 and 23, and the last two payments. How much interest did Larissa pay in total?

Quarterly payments of $3,000 are required on an $80,000 loan at 8.0% compounded quarterly. a) Calculate the interest component of Payment 30. b) Calculate the principal component of Payment 9. c) Calculate the final payment.

How much will the debtor owe after two years (just after the payment is made at the end of two years) ?

The interest rate on a $100,000 loan is 7.2% compounded semi-annually. The monthly payments on the loan are $700. a) Calculate the interest component of Payment 221. b) Calculate the principal component of Payment 156. c) Calculate the final payment.

A $25,000 home improvement (mortgage) loan charges interest at 6.6% compounded monthly for a three-year term. Monthly payments are based on a 10-year amortization and rounded up to the next $10. What will be the principal balance at the end of the first term?

The interest rate on a $100,000 mortgage loan is 7% compounded semi-annually. a) What are the monthly payments for a 25-year amortization? b) Suppose that the borrower instead makes weekly payments equal to one-fourth of the monthly payment calculated in part a. When will the loan be paid off if the interest rate does not change? Assume there are exactly 52 weeks in a year.

A $175,000 mortgage at 6.6% compounded semi-annually with a 25-year amortization requires monthly payments. The mortgage allows the borrower to prepay up to 10% of the original principal once each year. How much will the amortization period be shortened if, on the first anniversary of the mortgage, the borrower makes (in addition to the regular payment) a prepayment of: a) $10,000? b) $20,000?

A car loan is to be repaid by equal monthly payments for four years. The interest rate is 7.2% compounded monthly and the amount borrowed is $17,355. How much interest will be included in the first payment?

The interest rate on a $250,000 mortgage is 6.5% compounded monthly. Calculate the monthly payment for an amortization period of 15 and 20 years.

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much interest will the borrower pay over the six years?

A $100,000 loan and a $50,000 loan both have the same interest rate and the same amortization period (10 years). a) Will the monthly payment on the $100,000 loan be double the monthly payment on the $50,000 loan? Explain briefly. b) Will the balance after five years on the $100,000 loan be double the balance on the $50,000 loan? Explain briefly.

Five years ago, Ms. Halliday received a mortgage loan from the Bank of Nova Scotia for $60,000 at 7.8% compounded semi-annually for a five-year term. Monthly payments were based on a 25-year amortization. The bank is agreeable to renewing the loan for another five-year term at 5.8% compounded semi-annually. Calculate the principal reduction that will occur in the second five-year term if: a) The payments are recalculated based on the new interest rate and a continuation of the original 25-year amortization. b) Ms. Halliday continues to make the same payments as she made for the first five years (resulting in a reduction of the amortization period).

Semi-annual payments of $5,000 are to be made on a $70,000 loan at 14% compounded semi-annually. A smaller, final payment will be made at the end of the amortization period. What will be the size of the final payment?

The interest rate on a $6,400 loan is 10% compounded semi-annually. If the loan is to be repaid by monthly payments over a four-year term, prepare a partial amortization schedule showing details of the first two payments, Payments 34 and 35, and the last two payments.

The calculated monthly payment on a loan amortized over 10 years is rounded down by 0.3 cents to get to the nearest cent. a) Will the adjusted final payment be more than or less than the regular payment? b) Will the difference between the regular and the final payment be (pick one): (i) more than (ii) less than or (iii) equal to 0.3 cents? 120 = 36 cents? Explain.