6.5 Review Exercises

  1. 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

     

  2. 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

     

  3. 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

     

  4. 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]

     

  5. 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]

     

  6. 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

     

  7. 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

     

  8. Monthly payments are to be made against an $850,000 loan at 7.15% compounded annually with a 15-year amortization.
    1. What is the size of the monthly payment?
    2. Calculate the principal portion of the 100th payment.
    3. Calculate the interest portion of the 50th payment.
    4. Calculate how much the principal will be reduced in the second year.
    5. 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

     

  9. 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.
    1. What is the size of the quarterly payment?
    2. Calculate the principal portion of the 20th payment.
    3. Calculate the interest portion of the 33rd payment.
    4. Calculate how much the principal will be reduced in the second year.
    5. 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

     

  10. 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.
    1. Calculate the interest and principal portions in her first term.
    2. What is the balance remaining after the first term?
    3. What is the new mortgage payment amount in the second term?
    4. 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

     

  11. You have a $50,000 student loan at 3.1% compounded quarterly. You repay the loan with monthly payments of $750.
    1. How much interest is paid with the 20th payment?
    2. How much principal is paid with the 47th payment?
    3. What is the balance on the loan after five years?
    4. How much interest is paid in year four?
    5. How much principal is paid in year six?
    6. 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

     

  12. 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]

     

  13. 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

     

  14. 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

     

  15. 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.

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