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You and your spouse bought a house exactly 10 years ago. At that time, you have

ID: 2725727 • Letter: Y

Question

You and your spouse bought a house exactly 10 years ago. At that time, you have borrowed dollar 500,000 with a 30-year loan that requires a monthly mortgage payment. The interest rate was 6.0 percentage per year. Now, you want to convince your spouse to refinance the principal balance with a new 15-year loan with 4.8 percentage annual rate. How much is the new monthly payment? Should -you go ahead and refinance your loan? Assume that the opportunity cost of your money is 3.6 percentage per year. Ignore all transaction costs and assume that your first payment is one month from now.

Explanation / Answer

The monthly payment for the orginal loan is =pmt(rate,nper,pv) =pmt(0.06/12,360,500000)= 2,997.75

Hence the principal balance on the loan after 10 years is calculated as per the amortization balance below:

After 120 months, 10 years, the loan balance (principal) is $418,428.62

Nww the new interest rate is 4.8%. With this the new monthyly payment is =pmt(rate,nper,pv)

where rate = 0.048/12, nper =15*12 =180 and pv = 418,428.62

Hence monthly payment = pmt(0.048/12,180,418428.62) = $3,625.48

The monthly payment is higher since the new loan is for a shorter duration

Now the opportunity cost of money is 3.6% per annum. Asumming the opprtunity cost, we should not go ahead with the loan

Month Payment Interest Amortized Principal Balance 0 $         5,00,000.00 1 $ 2,997.75 2500 $     497.75 $         4,99,502.25 2 $ 2,997.75 2497.511 $     500.24 $         4,99,002.01 3 $ 2,997.75 2495.01 $     502.74 $         4,98,499.26 4 $ 2,997.75 2492.496 $     505.26 $         4,97,994.01 5 $ 2,997.75 2489.97 $     507.78 $         4,97,486.22 6 $ 2,997.75 2487.431 $     510.32 $         4,96,975.90 7 $ 2,997.75 2484.88 $     512.87 $         4,96,463.03 8 $ 2,997.75 2482.315 $     515.44 $         4,95,947.59 9 $ 2,997.75 2479.738 $     518.01 $         4,95,429.58 10 $ 2,997.75 2477.148 $     520.60 $         4,94,908.97 11 $ 2,997.75 2474.545 $     523.21 $         4,94,385.77 12 $ 2,997.75 2471.929 $     525.82 $         4,93,859.94 13 $ 2,997.75 2469.3 $     528.45 $         4,93,331.49 14 $ 2,997.75 2466.657 $     531.10 $         4,92,800.39 15 $ 2,997.75 2464.002 $     533.75 $         4,92,266.64 16 $ 2,997.75 2461.333 $     536.42 $         4,91,730.22 17 $ 2,997.75 2458.651 $     539.10 $         4,91,191.12 18 $ 2,997.75 2455.956 $     541.80 $         4,90,649.32 19 $ 2,997.75 2453.247 $     544.51 $         4,90,104.82 20 $ 2,997.75 2450.524 $     547.23 $         4,89,557.59 21 $ 2,997.75 2447.788 $     549.96 $         4,89,007.63 22 $ 2,997.75 2445.038 $     552.71 $         4,88,454.91 23 $ 2,997.75 2442.275 $     555.48 $         4,87,899.43 24 $ 2,997.75 2439.497 $     558.26 $         4,87,341.18 25 $ 2,997.75 2436.706 $     561.05 $         4,86,780.13 26 $ 2,997.75 2433.901 $     563.85 $         4,86,216.28 27 $ 2,997.75 2431.081 $     566.67 $         4,85,649.61 28 $ 2,997.75 2428.248 $     569.50 $         4,85,080.10 29 $ 2,997.75 2425.401 $     572.35 $         4,84,507.75 30 $ 2,997.75 2422.539 $     575.21 $         4,83,932.54 31 $ 2,997.75 2419.663 $     578.09 $         4,83,354.45 32 $ 2,997.75 2416.772 $     580.98 $         4,82,773.47 33 $ 2,997.75 2413.867 $     583.89 $         4,82,189.58 34 $ 2,997.75 2410.948 $     586.80 $         4,81,602.78 35 $ 2,997.75 2408.014 $     589.74 $         4,81,013.04 36 $ 2,997.75 2405.065 $     592.69 $         4,80,420.35 37 $ 2,997.75 2402.102 $     595.65 $         4,79,824.70 38 $ 2,997.75 2399.123 $     598.63 $         4,79,226.07 39 $ 2,997.75 2396.13 $     601.62 $         4,78,624.45 40 $ 2,997.75 2393.122 $     604.63 $         4,78,019.82 41 $ 2,997.75 2390.099 $     607.65 $         4,77,412.16 42 $ 2,997.75 2387.061 $     610.69 $         4,76,801.47 43 $ 2,997.75 2384.007 $     613.75 $         4,76,187.73 44 $ 2,997.75 2380.939 $     616.81 $         4,75,570.91 45 $ 2,997.75 2377.855 $     619.90 $         4,74,951.02 46 $ 2,997.75 2374.755 $     623.00 $         4,74,328.02 47 $ 2,997.75 2371.64 $     626.11 $         4,73,701.91 48 $ 2,997.75 2368.51 $     629.24 $         4,73,072.66 49 $ 2,997.75 2365.363 $     632.39 $         4,72,440.27 50 $ 2,997.75 2362.201 $     635.55 $         4,71,804.72 51 $ 2,997.75 2359.024 $     638.73 $         4,71,165.99 52 $ 2,997.75 2355.83 $     641.92 $         4,70,524.07 53 $ 2,997.75 2352.62 $     645.13 $         4,69,878.94 54 $ 2,997.75 2349.395 $     648.36 $         4,69,230.58 55 $ 2,997.75 2346.153 $     651.60 $         4,68,578.98 56 $ 2,997.75 2342.895 $     654.86 $         4,67,924.12 57 $ 2,997.75 2339.621 $     658.13 $         4,67,265.99 58 $ 2,997.75 2336.33 $     661.42 $         4,66,604.57 59 $ 2,997.75 2333.023 $     664.73 $         4,65,939.84 60 $ 2,997.75 2329.699 $     668.05 $         4,65,271.78 61 $ 2,997.75 2326.359 $     671.39 $         4,64,600.39 62 $ 2,997.75 2323.002 $     674.75 $         4,63,925.64 63 $ 2,997.75 2319.628 $     678.12 $         4,63,247.52 64 $ 2,997.75 2316.238 $     681.52 $         4,62,566.00 65 $ 2,997.75 2312.83 $     684.92 $         4,61,881.08 66 $ 2,997.75 2309.405 $     688.35 $         4,61,192.73 67 $ 2,997.75 2305.964 $     691.79 $         4,60,500.94 68 $ 2,997.75 2302.505 $     695.25 $         4,59,805.69 69 $ 2,997.75 2299.028 $     698.72 $         4,59,106.97 70 $ 2,997.75 2295.535 $     702.22 $         4,58,404.75 71 $ 2,997.75 2292.024 $     705.73 $         4,57,699.02 72 $ 2,997.75 2288.495 $     709.26 $         4,56,989.77 73 $ 2,997.75 2284.949 $     712.80 $         4,56,276.96 74 $ 2,997.75 2281.385 $     716.37 $         4,55,560.59 75 $ 2,997.75 2277.803 $     719.95 $         4,54,840.64 76 $ 2,997.75 2274.203 $     723.55 $         4,54,117.09 77 $ 2,997.75 2270.585 $     727.17 $         4,53,389.93 78 $ 2,997.75 2266.95 $     730.80 $         4,52,659.12 79 $ 2,997.75 2263.296 $     734.46 $         4,51,924.67 80 $ 2,997.75 2259.623 $     738.13 $         4,51,186.54 81 $ 2,997.75 2255.933 $     741.82 $         4,50,444.72 82 $ 2,997.75 2252.224 $     745.53 $         4,49,699.19 83 $ 2,997.75 2248.496 $     749.26 $         4,48,949.93 84 $ 2,997.75 2244.75 $     753.00 $         4,48,196.93 85 $ 2,997.75 2240.985 $     756.77 $         4,47,440.16 86 $ 2,997.75 2237.201 $     760.55 $         4,46,679.61 87 $ 2,997.75 2233.398 $     764.35 $         4,45,915.26 88 $ 2,997.75 2229.576 $     768.18 $         4,45,147.08 89 $ 2,997.75 2225.735 $     772.02 $         4,44,375.06 90 $ 2,997.75 2221.875 $     775.88 $         4,43,599.18 91 $ 2,997.75 2217.996 $     779.76 $         4,42,819.43 92 $ 2,997.75 2214.097 $     783.66 $         4,42,035.77 93 $ 2,997.75 2210.179 $     787.57 $         4,41,248.20 94 $ 2,997.75 2206.241 $     791.51 $         4,40,456.69 95 $ 2,997.75 2202.283 $     795.47 $         4,39,661.22 96 $ 2,997.75 2198.306 $     799.45 $         4,38,861.77 97 $ 2,997.75 2194.309 $     803.44 $         4,38,058.33 98 $ 2,997.75 2190.292 $     807.46 $         4,37,250.87 99 $ 2,997.75 2186.254 $     811.50 $         4,36,439.37 100 $ 2,997.75 2182.197 $     815.56 $         4,35,623.81 101 $ 2,997.75 2178.119 $     819.63 $         4,34,804.18 102 $ 2,997.75 2174.021 $     823.73 $         4,33,980.45 103 $ 2,997.75 2169.902 $     827.85 $         4,33,152.60 104 $ 2,997.75 2165.763 $     831.99 $         4,32,320.61 105 $ 2,997.75 2161.603 $     836.15 $         4,31,484.46 106 $ 2,997.75 2157.422 $     840.33 $         4,30,644.13 107 $ 2,997.75 2153.221 $     844.53 $         4,29,799.59 108 $ 2,997.75 2148.998 $     848.75 $         4,28,950.84 109 $ 2,997.75 2144.754 $     853.00 $         4,28,097.84 110 $ 2,997.75 2140.489 $     857.26 $         4,27,240.58 111 $ 2,997.75 2136.203 $     861.55 $         4,26,379.03 112 $ 2,997.75 2131.895 $     865.86 $         4,25,513.17 113 $ 2,997.75 2127.566 $     870.19 $         4,24,642.98 114 $ 2,997.75 2123.215 $     874.54 $         4,23,768.45 115 $ 2,997.75 2118.842 $     878.91 $         4,22,889.54 116 $ 2,997.75 2114.448 $     883.30 $         4,22,006.23 117 $ 2,997.75 2110.031 $     887.72 $         4,21,118.51 118 $ 2,997.75 2105.593 $     892.16 $         4,20,226.35 119 $ 2,997.75 2101.132 $     896.62 $         4,19,329.73 120 $ 2,997.75 2096.649 $     901.10 $         4,18,428.62