The Young family is purchasing a $130,000 house with a VA

Chapter 11, Problem 885

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The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25-year mortgage with an interest rate of 9.5%. They have $20,000 invested that could be used for a down payment. Since they do not need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000. a) Determine the total cost of the house with no down payment. b) Determine the total cost of the house if they make a down payment of $20,000. c) Mr. Young believes that the $20,000 investment will have an annual rate of return of 10% compounded quarterly. Assuming that Mr. Young is right, calculate the value of the investment in 25 years. (Use the compound interest formula on page 623.) d) If the Youngs use the $20,000 as a down payment, their monthly payments will decrease. Determine the difference of the monthly payments in parts (a) and (b). e) Assume that the difference in monthly payments, part (d), is invested each month at a rate of 6% compounded monthly for 25 years. Determine the value of the investment in 25 years. (Use the ordinary annuity formula on page 660.) f ) Use the information from parts (a)(e) to analyze the problem. Would you recommend that the Youngs make the down payment of $20,000 and invest the difference in their monthly payments as in part (e) or that they do not make the down payment and keep the $20,000 invested as in part (c)? Explain.