Larry Davis borrows $77,000 at 10 percent interest toward the purchase of a home
ID: 2657310 • Letter: L
Question
Larry Davis borrows $77,000 at 10 percent interest toward the purchase of a home. His mortgage is for 20 years. Use Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.) (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
b. How much interest will he pay over the life of the loan? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
c. How much should he be willing to pay to get out of a 10 percent mortgage and into a 8 percent mortgage with 20 years remaining on the mortgage? Assume current interest rates are 8 percent. Carefully consider the time value of money. Disregard taxes. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation / Answer
a. Annual payments will be computed using the formula: Annual payment = [P x R x (1+R)^N]/[(1+R)^N-1]
In the above formula P = $77,000, R = 10%, N = 20
Thus annual payment = [77,000*10%*(1+10%)^20]/(1+10%)^20-1]
= 51,801.75/5.73 = $9,044.39
b. Interest calculation and table has been shown below:
Thus total interest = $103,887.82
c. If rate is changed to 8% then total interest payment will decline. The table below shows the new amount of total interest @8%:
Here the new annual payments will be = [77,000*8%*(1+8%)^20]/(1+8%)^20-1] = $7842.62
The difference in values = 9044.39 - 7842.62 = $1201.77
PVIFA at 8% and 20 years = 9.8181 (from PVIFA table)
Thus present value of difference = 1201.77*9.8181
= $11,799.10. This is the amount that he will be willing to pay to get out of a 10 percent mortgage and into a 8 percent mortgage with 20 years remaining on the mortgage
Year Annual Payment Opening balance of loan Interest @ 10% on opening balance of loan Principal = Annual payment - interest Closing balance of loan = opening balance of loan - principal payment 1 9,044.39 77,000.00 7,700.00 1,344.39 75,655.61 2 9,044.39 75,655.61 7,565.56 1,478.83 74,176.78 3 9,044.39 74,176.78 7,417.68 1,626.71 72,550.07 4 9,044.39 72,550.07 7,255.01 1,789.38 70,760.68 5 9,044.39 70,760.68 7,076.07 1,968.32 68,792.36 6 9,044.39 68,792.36 6,879.24 2,165.16 66,627.20 7 9,044.39 66,627.20 6,662.72 2,381.67 64,245.53 8 9,044.39 64,245.53 6,424.55 2,619.84 61,625.69 9 9,044.39 61,625.69 6,162.57 2,881.82 58,743.87 10 9,044.39 58,743.87 5,874.39 3,170.00 55,573.87 11 9,044.39 55,573.87 5,557.39 3,487.00 52,086.86 12 9,044.39 52,086.86 5,208.69 3,835.70 48,251.16 13 9,044.39 48,251.16 4,825.12 4,219.28 44,031.88 14 9,044.39 44,031.88 4,403.19 4,641.20 39,390.68 15 9,044.39 39,390.68 3,939.07 5,105.32 34,285.36 16 9,044.39 34,285.36 3,428.54 5,615.86 28,669.50 17 9,044.39 28,669.50 2,866.95 6,177.44 22,492.06 18 9,044.39 22,492.06 2,249.21 6,795.18 15,696.88 19 9,044.39 15,696.88 1,569.69 7,474.70 8,222.17 20 9,044.39 8,222.17 822.22 8,222.17 0.00 Total 103,887.82Related Questions
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