Review Exercises 

1. Quinn placed $33,000 into a five-year ordinary investment annuity earning 7.75% compounded quarterly. He will be receiving quarterly payments. Calculate the principal and interest components of the sixth payment. (Answer: PRN = $1,504.27; INT = $501.75)

2. Annanya took out a $42,500 ordinary loan at 6.6% compounded monthly with monthly payments over the six-year amortization period. Calculate the total principal and interest portions for the third year. (Answer: PRN = $6,810.95; INT = $1,786.45)

3. Two years ago, Sumandeep invested $20,000 at 9.45% compounded monthly. She has been receiving end-of-month payments since, and the last payment will be today. Calculate the amount of the final payment. (Answer: $917.82)

4. Hogwild Industries borrowed $75,000 to purchase some new equipment. The terms of the ordinary loan require quarterly payments for three years with an interest rate of 7.1% compounded semi-annually. Calculate the total interest and principal portions for the third year. (Answer: PRN = $26,763.03; INT = $1,187.52)

5. Kerry, who is a pharmacist, just became a new franchisee for Shoppers Drug Mart. As part of her franchising agreement, her operation is to assume a $1.2 million mortgage to be financed over the next 15 years. She is to make payments after every six months. Head office will charge her a rate of 14.25% compounded annually. Determine the amount of her mortgage payment. (Answer: $95,615.95)

6. Alibaba took out a 25-year amortization $273,875 mortgage five years ago at 4.85% compounded semi-annually and has been making monthly payments. He will renew the mortgage for a three-year term today at an interest rate of 6.1% compounded semi-annually on the same amortization schedule. What are his new monthly mortgage payments? (Answer: $1,735.84)

Applications

7. Monthly payments are to be made against an $850,000 loan at 7.15% compounded annually with a 15-year amortization.
   a) What is the size of the monthly payment? (Answer: PMT = $7,604.85)
   b) Calculate the principal portion of the 100th payment. (Answer: PRN = $4,771.37)
   c) Calculate the interest portion of the 50th payment. (Answer: INT = $4,026.56)
   d) Calculate how much the principal will be reduced in the second year. (Answer: PRN = $35,827.23)
   e) Calculate the total interest paid in the fifth year. (Answer: INT = $47,183.46)

8. An investment annuity of $100,000 earning 4.5% compounded quarterly is to make payments at the end of every three months with a 10-year amortization.
   a) What is the size of the quarterly payment? (Answer: PMT = $3,118.35)
   b) Calculate the principal portion of the 20th payment. (Answer: PRN = $2,465.45)
   c) Calculate the interest portion of the 33rd payment. (Answer: INT = $266.96)
   d) Calculate how much the principal will be reduced in the second year. (Answer: PRN = $8,480.07)
   e) Calculate the total interest paid in the seventh year. (Answer: INT = $1,866.95)

9. A retail credit card allows its users to make purchases and pay off the debts through month-end payments equally spread over four months. The interest rate is 28.8% compounded annually on such purchases. A customer just placed $1,000 on the card and intends to use this plan.
   a) What is the amount of the final payment? (Answer: $263.47)
   b) Calculate the total interest incurred by using the payment plan. (Answer: $53.85)

10. Shelley Shearer Dance School took out a mortgage in Winnipeg for $500,000 on a five-year term with a 20-year amortization. The mortgage rate is 4.89% compounded semi-annually. Calculate the weekly mortgage payment amount. (Answer: $750.22)

Challenge, Critical Thinking, & Other Applications

11. Five years ago, the Staples signed a closed fixed rate mortgage with a 25-year amortization and monthly payments. They negotiated an interest rate of 4.49% compounded semi-annually. The terms of the mortgage allow for the Staples to make a single top-up payment at any one point throughout the term. The mortgage principal was $179,000 and they made one top-up payment of $10,000 three years into the term. They are renewing the mortgage today for another five-year term but have reduced the amortization period by five years.
    a) What is the balance remaining at the end of the first term? (Answer: $146,200.92)
    b) By what amount was the interest portion of the first term reduced by making the top-up payment? (Answer: $928.70)
    c) Calculate the mortgage payment amount for the second term if the interest rate remains unchanged. (Answer: $1,511.58)