Paying Off That Dream House When Jacqueline and Keith Sommers were \"house hunti
ID: 2809875 • Letter: P
Question
Paying Off That Dream House When Jacqueline and Keith Sommers were "house hunting" five years ago, the mortgage rates were pretty high. The fixed rate on a 30-year mort- gage was 7.25%, while the 15-year fixed rate was at 6.25%. After walking through many homes, they finally reached a consensus and decided to buy a $300,000, two-story house in an up-and-coming suburban neighborhood in the Midwest. To avoid prepaid mortgage insurance (PMI), the couple had to borrow from family members and come up with a 20% down pay- ment and the additional required closing costs. Since Jacqueline and Keith had already accumulated significant credit card debt and were still paying off their college loans, they decided to opt for lower monthly payments by taking on a 30-year mortgage, despite its higher interest rate. Currently, due to worsening economic conditions, mortgage rates have come down significantly and a refinancing frenzy is underway. Jacqueline and Keith have seen 15-year fixed rates (with no closing costs) advertised at 2.75%, and 30-year rates at 3.75%. Jacqueline and Keith realize that refinancing is quite a hassle due to all the paperwork involved, but with rates being down to 30-year lows they don't want to let this opportunity pass them by. About two years ago, rates were down to similar levels, but they procrastinated and missed the boat. This time, however, the couple called their mortgage officer at the Uptown Bank and locked in the 2.75%, 15-year rate. Nothing was going to stop them from reducing the costs of paying off their dream house this time!Explanation / Answer
Value of House = $ 300,000
Down Payment = 20% of $ 300,000 = $ 60,000
Loan Availed = $ 300,000 - $ 60,000 = $ 240,000
Mortgage Duration = 30 years
N, Number of months =12*30 =360 ( As payments are made on a monthly basis)
ROI on yearly basis = 7.25% p.a.
ROI on monthly basis = 7.25% /12 = 0.60% p.m.
Amortization table for reference is drawn at the end of the answer.
1. Jacqueline and Keith's monthly mortgage payments prior to refinancing are nothing but EMI(Equated Monthly Installment)
So, here we calculate EMI.
To calculate EMI we would use formula
EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
where P is the Principle Loan Amount of $ 240,000.
R is rate of interest calualted on monthly basis it should be = 7.25% /12 = 0.60%
N is tenture in number of months = Duration of laon in years * 12= 30*12 = 360
EMI = $ 240,000*0.60% *(1 + 0.60% )360/((1 + 0.60% )360 - 1)
= $1,637.22
So, Jacqueline and Keith's monthly mortgage payments prior to refinancing are $ 1,637.22.
2.
Amount of money paid towards interest in the first five years.
Interest for period 1 = Principal at the end of previous period * ROI
= $ 400,000 * 0.35% = $ 1,416.67
Similary we have to calculate for period 2, period 3, and upto period 60.
Calculated figures are shown in the table.
Interest paid = Sum of all the interest for first 60 periods = $ 84, 742.45
Amount of money paid towards mortgage in first five years.
The portion to mortgage for period 1 = EMI - Interest for period 1
= $3,009.11 - $ 1,416.67
= $1,592.45
Similary we have to calculate for period 2, period 3, and upto period 60.
Calculated figures are shown in the table.
Mortgage paid = Sum of all the mortgage for first 60 periods = $ 13,490.93
Period No Monthly Mortgage Payment Interest for Period Portion to Mortgage Mortgage at End of period. 0 _ _ _ $240,000.00 1 $1,637.22 $ 1,450.00 $187.22 $239,812.78 2 $1,637.22 $ 1,448.87 $188.35 $239,624.42 3 $1,637.22 $ 1,447.73 $189.49 $239,434.93 4 $1,637.22 1446.586 190.64 239244.29 5 $1,637.22 1445.4343 191.79 239052.50 6 $1,637.22 1444.2755 192.95 238859.56 7 $1,637.22 1443.1098 194.11 238665.44 8 $1,637.22 1441.9371 195.29 238470.16 9 $1,637.22 1440.7572 196.47 238273.69 10 $1,637.22 1439.5702 197.65 238076.04 11 $1,637.22 1438.3761 198.85 237877.19 12 $1,637.22 1437.1747 200.05 237677.14 13 $1,637.22 1435.9661 201.26 237475.89 14 $1,637.22 1434.7501 202.47 237273.41 15 $1,637.22 1433.5269 203.70 237069.72 16 $1,637.22 1432.2962 204.93 236864.79 17 $1,637.22 1431.0581 206.16 236658.63 18 $1,637.22 1429.8125 207.41 236451.22 19 $1,637.22 1428.5594 208.66 236242.55 20 $1,637.22 1427.2987 209.92 236032.63 21 $1,637.22 1426.0305 211.19 235821.43 22 $1,637.22 1424.7545 212.47 235608.97 23 $1,637.22 1423.4708 213.75 235395.21 24 $1,637.22 1422.1794 215.04 235180.17 25 $1,637.22 1420.8802 216.34 234963.83 26 $1,637.22 1419.5731 217.65 234746.18 27 $1,637.22 1418.2582 218.96 234527.21 28 $1,637.22 1416.9352 220.29 234306.92 29 $1,637.22 1415.6043 221.62 234085.31 30 $1,637.22 1414.2654 222.96 233862.35 31 $1,637.22 1412.9184 224.30 233638.04 32 $1,637.22 1411.5632 225.66 233412.38 33 $1,637.22 1410.1998 227.02 233185.36 34 $1,637.22 1408.8282 228.39 232956.97 35 $1,637.22 1407.4483 229.77 232727.19 36 $1,637.22 1406.0601 231.16 232496.03 37 $1,637.22 1404.6635 232.56 232263.47 38 $1,637.22 1403.2585 233.96 232029.50 39 $1,637.22 1401.8449 235.38 231794.13 40 $1,637.22 1400.4228 236.80 231557.33 41 $1,637.22 1398.9922 238.23 231319.09 42 $1,637.22 1397.5529 239.67 231079.42 43 $1,637.22 1396.1049 241.12 230838.31 44 $1,637.22 1394.6481 242.57 230595.73 45 $1,637.22 1393.1825 244.04 230351.69 46 $1,637.22 1391.7081 245.51 230106.18 47 $1,637.22 1390.2248 247.00 229859.18 48 $1,637.22 1388.7325 248.49 229610.69 49 $1,637.22 1387.2312 249.99 229360.69 50 $1,637.22 1385.7209 251.50 229109.19 51 $1,637.22 1384.2014 253.02 228856.17 52 $1,637.22 1382.6727 254.55 228601.62 53 $1,637.22 1381.1348 256.09 228345.53 54 $1,637.22 1379.5876 257.64 228087.90 55 $1,637.22 1378.031 259.19 227828.70 56 $1,637.22 1376.4651 260.76 227567.95 57 $1,637.22 1374.8897 262.33 227305.61 58 $1,637.22 1373.3047 263.92 227041.70 59 $1,637.22 1371.7102 265.51 226776.18 60 $1,637.22 1370.1061 267.12 226509.07 Sum 84742.45 13490.93Related Questions
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