10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 641 f) Determine how much of the first payment on the mortgage is applied to the principal. $62.34 g) Determine the total amount she pays for the condominium. (Do not include taxes or homeowners’ insurance.) $218,203 h) Determine the total interest paid. $123,203 Challenge Problems/Group Activities 33. Changing Lengths of Mortgages Rose and George are purchasing a house for $450,000. Their bank requires them to pay a down payment of 20%, The current mortgage rate is 10%, and they are required to pay 1 point at the time of closing. Determine the total amount Rose and George will pay for their house, including principal, interest, down payment, and points (do not include taxes and homeowners’ insurance) if the length of their mortgage is a) 10 years. $664,491.60 b) 20 years. $927,379.20 c) 30 years. $1,230,933.60 34. Comparing Payment Frequency Janet is purchasing a new house for $315,000. Her credit union requires her to make a 20% down payment, and the current mortgage rate is 6%. Janet is exploring different 10-year mortgage payment options. Use the principal and interest formula to determine Janet’s principal and interest payment if she makes her payments a) Monthly. $2797.72 b) Bimonthly (use n 24 = ). $1397.59 c) Weekly (use n 52 = ). $644.72 35. Comparing Mortgages The Hassads are applying for a $90,000 mortgage. They can choose between a 30-year conventional mortgage and a 30-year variablerate mortgage. The interest rate on a 30-year conventional mortgage is 9.5%. The terms of the variable-rate mortgage are 6.5% interest rate the first year, an annual cap of 1%, and an aggregate cap of 6%. The interest rates and the mortgage payments are adjusted annually. Assume that the interest rates for the variable-rate mortgage increase by the maximum amount each year. Then the monthly mortgage payments for the variable-rate mortgage for years 1– 6 are $568.86, $629.29, $692.02, $756.77, $823.27, and $891.26, respectively. a) Knowing that they will be in the house for only 6 years, which mortgage, the conventional mortgage or the variable-rate mortgage, will be the least expensive for that period? The variable-rate mortgage b) How much will they save by choosing the less expensive mortgage? $2149.80 Research Activities 36. Dream Home Search in your area to find your “dream home” that is for sale and note the asking price. Next, search the websites of local lenders to find the best interest rates for both a 15-year fixed mortgage and a 30-year fixed mortgage. Assume that you make a 20% down payment; then calculate and compare the monthly payments of principal and interest for both the 15-year mortgage and the 30-year mortgage. Using an amortization calculator (see page 636), compare the total amount of interest paid on the 15-year mortgage and on the 30-year mortgage. Write a report summarizing your findings. 37. Closing Costs The closing of a house involves many additional costs for the both the buyer and the seller. Select a home that is for sale and note the asking price. Do research and use this asking price to calculate the closing costs in your area. A partial list of closing costs include: title search fee, title insurance fee, credit report fee, loan origination fee, attorney’s fees, inspection fee, appraisal fee, survey fee, escrow account deposits, pest inspection fee, recording fee, and underwriting fees. 38. Credit Scores Read the Mathematics Today on page 632 regarding credit scores. Do research and write a report on how lenders use credit scores. Be specific about what range of credit scores are required to obtain various loans or to obtain a credit card. Include information provided by all three major credit bureaus. In Sections 10.2 and 10.3, we studied simple and compound interest, respectively. In both sections, we answered questions involving the investment of one lump sum of money. Although such questions may be relevant to our everyday financial matters, more appropriate questions might involve investing smaller amounts of money on a regular basis over a longer period of time. For example, the Brabsons, who are planning for retirement, might ask the question: If we deposit $100 a month at a 5% interest rate compounded Ordinary Annuities, Sinking Funds, and Retirement Investments SECTION 10.6 LEARNING GOALS Upon completion of this section, you will be able to: 7 Solve problems involving ordinary annuities. 7 Solve problems involving sinking funds. 7 Understand other annuities and retirement savings options. Robert Kneschke/Shutterstock
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