# 6.5 Review Exercises

- Annanya took out a $42,500 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.

**Click to see Answer**PRN=$6,810.95, INT=$1,786.45

- Two years ago, Sumandeep borrowed $20,000 at 9.45% compounded monthly. She has been paying end-of-month payments since, and the last payment will be today. Calculate the amount of the final payment.

**Click to see Answer**$917.82

- 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.

**Click to see Answer**PRN=$26,763.03, INT=$1,187.52

- Dr. Strong of Island Lakes Dental Centre acquired a new Panoramic X-ray machine for his practice. The $7,400 for the machine, borrowed at 8.8% compounded annually, is to be repaid in four end-of-quarter instalments. Develop a complete amortization schedule and total the interest paid.

**Click to see Answer****Payment Number****Payment****Interest Paid (INT)****Principal Paid (PRN)****Balance (BAL)**0 [latex]\$7,400[/latex] 1 [latex]\$1,949.59[/latex] [latex]\$157.69[/latex] [latex]\$1,791.90[/latex] [latex]\$5,608.10[/latex] 2 [latex]\$1,949.59[/latex] [latex]\$119.50[/latex] [latex]\$1,830.09[/latex] [latex]\$3,778.01[/latex] 3 [latex]\$1,949.59[/latex] [latex]\$80.51[/latex] [latex]\$1,869.08[/latex] [latex]\$1,908.93[/latex] 4 [latex]\$1,949.61[/latex] [latex]\$40.68[/latex] [latex]\$1,908.93[/latex] [latex]\$0[/latex] **Totals**[latex]\$7,798.38[/latex] [latex]\$398.38[/latex] [latex]\$7,400[/latex] - Dr. Miller acquired a new centrifuge machine from Liaoyang Longda Pharmaceutical Machinery Company (LLPMC) for his medical practice. He is to pay off the $60,341 through 20 month-end payments. LLPMC has set the interest rate on the loan at 9.5% compounded quarterly. Develop a partial amortization schedule for the third to sixth payments.

**Click to see Answer****Payment Number****Payment****Interest Paid (INT)****Principal Paid (PRN)****Balance (BAL)**3 [latex]\$3,272.05[/latex] [latex]\$429.84[/latex] [latex]\$2,842.21[/latex] [latex]\$51,880.64[/latex] 4 [latex]\$3,272.05[/latex] [latex]\$407.51[/latex] [latex]\$2,864.54[/latex] [latex]\$49,016.11[/latex] 5 [latex]\$3,272.05[/latex] [latex]\$385.01[/latex] [latex]\$2,887.04[/latex] [latex]\$46,129.07[/latex] 6 [latex]\$3,272.05[/latex] [latex]\$362.33[/latex] [latex]\$2,909.72[/latex] [latex]\$43,219.35[/latex] - 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.

**Click to see Answer**$95,615.95

- 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?

**Click to see Answer**$1,735.84

- Monthly payments are to be made against an $850,000 loan at 7.15% compounded annually with a 15-year amortization.
- What is the size of the monthly payment?
- Calculate the principal portion of the 100th payment.
- Calculate the interest portion of the 50th payment.
- Calculate how much the principal will be reduced in the second year.
- Calculate the total interest paid in the fifth year.

**Click to see Answer**a. $7,604.85; b. $4,771.37; c. $4,026.56; d. $35,827.23; e. $47,183.46

- 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.
- What is the size of the quarterly payment?
- Calculate the principal portion of the 20th payment.
- Calculate the interest portion of the 33rd payment.
- Calculate how much the principal will be reduced in the second year.
- Calculate the total interest paid in the seventh year.

**Click to see Answer**a. $3,118.35; b. $2,465.45; c. $166.96; d. $8,480.07; e. $1,866.95

- Four years ago, Katrina became a landlord and opened her new four-unit apartment housing unit with an initial mortgage at 6.83% compounded semi-annually in the amount of $971,000 less a $100,000 down payment. She amortized over 30 years and opted for monthly payments. Upon renewing her mortgage today, she is taking a two-year term at 5.1% compounded semi-annually while continuing with monthly payments and the original amortization timeline.
- Calculate the interest and principal portions in her first term.
- What is the balance remaining after the first term?
- What is the new mortgage payment amount in the second term?
- What is the balance remaining after the second term?

**Click to see Answer**a. PRN=$ 41,301.88, INT=$229,441.64; b. $829,698.12; c. $4,779.82; d. $797,181.08

- You have a $50,000 student loan at 3.1% compounded quarterly. You repay the loan with monthly payments of $750.
- How much interest is paid with the 20th payment?
- How much principal is paid with the 47th payment?
- What is the balance on the loan after five years?
- How much interest is paid in year four?
- How much principal is paid in year six?
- What is the size of your final payment?

**Click to see Answer**a. $97.71; b. $699.23; c. $9,750.63; d. $705.58; e. $8,822.85; f. $180.64

- John received a $80,000 loan at 4.96% compounded semi-annually. He made quarterly payments of $3,000 to repay the loan. Construct a partial amortization schedule showing the details of the last two payments and the totals.

**Click to see Answer****Payment Number****Payment****Interest Paid (INT)****Principal Paid (PRN)****Balance (BAL)**32 [latex]\$3,000[/latex] [latex]\$55.70[/latex] [latex]\$2,944.30[/latex] [latex]\$1,575.34[/latex] 33 [latex]\$1,594.75[/latex] [latex]\$19.41[/latex] [latex]\$1,575.34[/latex] [latex]\$0[/latex] **Totals**[latex]\$97,594.75[/latex] [latex]\$17,594.75[/latex] [latex]\$80,000[/latex] - You purchased a $400,000 house. You paid 10% as a down payment and took out a mortgage for the balance at 4.5% compounded semi-annually. You repaid the mortgage with monthly payments for 25 years. How much is the amortization period shortened by if a lump-sum payment of $15,000 is made at the end of the fourth year?

**Click to see Answer**1 year, 6 months

- A $525,000 mortgage at 3.9% compounded semi-annually is repaid with monthly payments for 25 years. How much is the amortization period shortened by if the monthly payments are increased by $200 at the end of year three?

**Click to see Answer**2 years, 3 months

- A $600,000 mortgage at 2.75% compounded semi-annually is repaid with monthly payments of $2,445 for 30 years. How much is the amortization period shortened by if mortgage is repaid with semi-monthly payments of $1,300 instead of the monthly payments?

**Click to see Answer**2 years, 8 months

#### Attribution

“Chapter 13 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.