# 3.5 Review Exercises

## Chapter 3 Review Exercises

- Annanya took out a [latex]\$42,500[/latex] loan at [latex]6.6\%[/latex] compounded monthly with monthly payments over the six-year amortization period. Calculate the total principal and interest portions for the third year.

**Solution**[latex]PRN=\$6,810.95[/latex], [latex]INT=\$1,786.45[/latex]

- Two years ago, Sumandeep borrowed [latex]\$20,000[/latex] at [latex]9.45\%[/latex] 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.

**Solution**[latex]\$917.82[/latex]

- Hogwild Industries borrowed [latex]\$75,000[/latex] to purchase some new equipment. The terms of the ordinary loan require quarterly payments for three years with an interest rate of [latex]7.1\%[/latex] compounded semi-annually. Calculate the total interest and principal portions for the third year.

**Solution**[latex]PRN=\$26,763.03[/latex], [latex]INT=\$1,187.52[/latex]

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

**Solution****Payment Number****Payment****Interest Paid (INT)****Principal Paid (PRN)****Balance (BAL)**[latex]0[/latex] [latex]\$7,400[/latex] [latex]1[/latex] [latex]\$1,949.59[/latex] [latex]\$157.69[/latex] [latex]\$1,791.90[/latex] [latex]\$5,608.10[/latex] [latex]2[/latex] [latex]\$1,949.59[/latex] [latex]\$119.50[/latex] [latex]\$1,830.09[/latex] [latex]\$3,778.01[/latex] [latex]3[/latex] [latex]\$1,949.59[/latex] [latex]\$80.51[/latex] [latex]\$1,869.08[/latex] [latex]\$1,908.93[/latex] [latex]4[/latex] [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 [latex]\$60,341[/latex] through [latex]20[/latex] month-end payments. LLPMC has set the interest rate on the loan at [latex]9.5\%[/latex] compounded quarterly. Develop a partial amortization schedule for the third to sixth payments.

**Solution****Payment Number****Payment****Interest Paid (INT)****Principal Paid (PRN)****Balance (BAL)**[latex]3[/latex] [latex]\$3,272.05[/latex] [latex]\$429.84[/latex] [latex]\$2,842.21[/latex] [latex]\$51,880.64[/latex] [latex]4[/latex] [latex]\$3,272.05[/latex] [latex]\$407.51[/latex] [latex]\$2,864.54[/latex] [latex]\$49,016.11[/latex] [latex]5[/latex] [latex]\$3,272.05[/latex] [latex]\$385.01[/latex] [latex]\$2,887.04[/latex] [latex]\$46,129.07[/latex] [latex]6[/latex] [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 [latex]\$1.2[/latex] million mortgage to be financed over the next [latex]15[/latex] years. She is to make payments after every six months. Head office will charge her a rate of [latex]14.25\%[/latex] compounded annually. Determine the amount of her mortgage payment.

**Solution**[latex]\$95,615.95[/latex]

- Alibaba took out a 25-year amortization [latex]\$273,875[/latex] mortgage five years ago at [latex]4.85\%[/latex] 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 [latex]6.1\%[/latex] compounded semi-annually on the same amortization schedule. What are his new monthly mortgage payments?

**Solution**[latex]\$1,735.84[/latex]

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

**Solution**a. [latex]\$7,604.85[/latex]; b. [latex]\$4,771.37[/latex]; c. [latex]\$4,026.56[/latex]; d. [latex]\$35,827.23[/latex]; e. [latex]\$47,183.46[/latex]

- An investment annuity of [latex]\$100,000[/latex] earning [latex]4.5\%[/latex] 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 [latex]20^{th}[/latex] payment.
- Calculate the interest portion of the [latex]33^{rd}[/latex] payment.
- Calculate how much the principal will be reduced in the second year.
- Calculate the total interest paid in the seventh year.

**Solution**a. [latex]\$3,118.35[/latex]; b. [latex]\$2,465.45[/latex]; c. [latex]\$166.96[/latex]; d. [latex]\$8,480.07[/latex]; e. [latex]\$1,866.95[/latex]

- Four years ago, Katrina became a landlord and opened her new four-unit apartment housing unit with an initial mortgage at [latex]6.83\%[/latex] compounded semi-annually in the amount of [latex]\$971,000[/latex] less a [latex]\$100,000[/latex] down payment. She amortized over [latex]30[/latex] years and opted for monthly payments. Upon renewing her mortgage today, she is taking a two-year term at [latex]5.1\%[/latex] 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?

**Solution**a. [latex]PRN=\$ 41,301.88[/latex], [latex]INT=\$229,441.64[/latex]; b. [latex]\$829,698.12[/latex]; c. [latex]\$4,779.82[/latex]; d. [latex]\$797,181.08[/latex]

- You have a [latex]\$50,000[/latex] student loan at [latex]3.1\%[/latex] compounded quarterly. You repay the loan with monthly payments of [latex]\$750[/latex].
- How much interest is paid with the [latex]20^{th}[latex] payment?
- How much principal is paid with the [latex]47^{th}[latex] 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?

**Solution**a. [latex]\$97.71[/latex]; b. [latex]\$699.23[/latex]; c. [latex]\$9,750.63[/latex]; d. [latex]\$705.58[/latex]; e. [latex]\$8,822.85[/latex]; f. [latex]\$180.64[/latex]

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

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

**Solution**[latex]1[/latex] year, [latex]6[/latex] months

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

**Solution**[latex]2[/latex] years, [latex]3[/latex] months

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

**Solution**[latex]2[/latex] years, [latex]8[/latex] 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.