3.5 Review Exercises

Chapter 3 Review Exercises

  1. 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]

  2. 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]

  3. 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]

  4. 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]
  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 [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]
  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 [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]

  7. 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]

  8. 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.
    1. What is the size of the monthly payment?
    2. Calculate the principal portion of the [latex]100^{th}[/latex] payment.
    3. Calculate the interest portion of the [latex]50^{th}[/latex] payment.
    4. Calculate how much the principal will be reduced in the second year.
    5. 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]

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

  10. 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.
    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?
    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]

  11. 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].
    1. How much interest is paid with the [latex]20^{th}[latex] payment?
    2. How much principal is paid with the [latex]47^{th}[latex] 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?
    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]

  12. 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]
  13. 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

  14. 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

  15. 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

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