# 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)
1. 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)
1. 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)
1. 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)
1. 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)
1. 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

1. 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)
1. 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)
1. 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)
1. 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

1. 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)

## License

Business Math: A Step-by-Step Handbook Abridged Copyright © 2022 by Sanja Krajisnik; Carol Leppinen; and Jelena Loncar-Vines is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.