A house can be purchased for $140000, and you have $10000 cash for a down payment....
A house can be purchased for $140000, and you have $10000 cash for a down payment. You are considering the following two financing options: bullet Option 1. Getting a new standard mortgage with a 7.5% (APR) interest and a 30-year term. bullet Option 2. Assuming the seller's old mortgage, which has an interest rate of 5.5% (APR), a remaining term of 25 years (the original term was 30 years), a remaining balance of $92 comma 983, and payments of $571 per month. You can obtain a second mortgage for the remaining balance ($37 comma 017) from your credit union at 9% (APR) with a 10-year repayment period.
(a) What is the effective interest rate of the combinedmortgage?
b) Compute the monthly payments for each option over the life of the mortgage.
(c) Compute the total interest payment for each option.
(d) What homeowner’s interest rate makes the two financing options equivalent?
Homework Answers
Option 1-
| Interest rate | 7.50% |
| Tenor (years) | 30 |
| Loan value | 130000 |
| EMI | PMT(7.5%,30,-130000) |
| Repayment schedule | Opening o/s (i) | EMI (ii) | Interest (iii) [(i)*7.5%] |
Principal (iv) [(ii)-(iii)] |
O/s
(v) [(i)-(iv)] |
| Loan - Year 1 | 130000.00 | 11007.26 | 9,750.00 | 1257.26 | 128742.74 |
| Year 2 | 128742.74 | 11007.26 | 9,655.71 | 1351.56 | 127391.18 |
| Year 3 | 127391.18 | 11007.26 | 9,554.34 | 1452.92 | 125938.26 |
| Year 4 | 125938.26 | 11007.26 | 9,445.37 | 1561.89 | 124376.37 |
| Year 5 | 124376.37 | 11007.26 | 9,328.23 | 1679.03 | 122697.34 |
| Year 6 | 122697.34 | 11007.26 | 9,202.30 | 1804.96 | 120892.38 |
| Year 7 | 120892.38 | 11007.26 | 9,066.93 | 1940.33 | 118952.05 |
| Year 8 | 118952.05 | 11007.26 | 8,921.40 | 2085.86 | 116866.19 |
| Year 9 | 116866.19 | 11007.26 | 8,764.96 | 2242.30 | 114623.89 |
| Year 10 | 114623.89 | 11007.26 | 8,596.79 | 2410.47 | 112213.42 |
| Year 11 | 112213.42 | 11007.26 | 8,416.01 | 2591.25 | 109622.17 |
| Year 12 | 109622.17 | 11007.26 | 8,221.66 | 2785.60 | 106836.57 |
| Year 13 | 106836.57 | 11007.26 | 8,012.74 | 2994.52 | 103842.05 |
| Year 14 | 103842.05 | 11007.26 | 7,788.15 | 3219.11 | 100622.95 |
| Year 15 | 100622.95 | 11007.26 | 7,546.72 | 3460.54 | 97162.41 |
| Year 16 | 97162.41 | 11007.26 | 7,287.18 | 3720.08 | 93442.33 |
| Year 17 | 93442.33 | 11007.26 | 7,008.17 | 3999.09 | 89443.24 |
| Year 18 | 89443.24 | 11007.26 | 6,708.24 | 4299.02 | 85144.22 |
| Year 19 | 85144.22 | 11007.26 | 6,385.82 | 4621.44 | 80522.78 |
| Year 20 | 80522.78 | 11007.26 | 6,039.21 | 4968.05 | 75554.73 |
| Year 21 | 75554.73 | 11007.26 | 5,666.60 | 5340.66 | 70214.07 |
| Year 22 | 70214.07 | 11007.26 | 5,266.06 | 5741.21 | 64472.87 |
| Year 23 | 64472.87 | 11007.26 | 4,835.47 | 6171.80 | 58301.07 |
| Year 24 | 58301.07 | 11007.26 | 4,372.58 | 6634.68 | 51666.39 |
| Year 25 | 51666.39 | 11007.26 | 3,874.98 | 7132.28 | 44534.11 |
| Year 26 | 44534.11 | 11007.26 | 3,340.06 | 7667.20 | 36866.91 |
| Year 27 | 36866.91 | 11007.26 | 2,765.02 | 8242.24 | 28624.66 |
| Year 28 | 28624.66 | 11007.26 | 2,146.85 | 8860.41 | 19764.25 |
| Year 29 | 19764.25 | 11007.26 | 1,482.32 | 9524.94 | 10239.31 |
| Year 30 | 10239.31 | 11007.26 | 767.95 | 10239.31 | 0.00 |
| 2,00,217.82 |
Interest rate = 200217.82/130000 = 154%
Option 2
| EMI | 6931.82 | PMT(5.5%,30,-92983) |
| Loan balance | 92983 | |
| interest rate | 5.50% | |
| Balance tenor | 25 |
| Repayment schedule | Opening o/s (i) | EMI (ii) | Interest (iii) [(i)*7.5%] |
Principal (iv) [(ii)-(iii)] |
O/s (v) [(i)-(iv)] |
| Loan - Year 1 | 92,983.00 | 6,931.82 | 5,114.07 | 1,817.76 | 91,165.24 |
| Year 2 | 91,165.24 | 6,931.82 | 5,014.09 | 1,917.73 | 89,247.51 |
| Year 3 | 89,247.51 | 6,931.82 | 4,908.61 | 2,023.21 | 87,224.30 |
| Year 4 | 87,224.30 | 6,931.82 | 4,797.34 | 2,134.49 | 85,089.81 |
| Year 5 | 85,089.81 | 6,931.82 | 4,679.94 | 2,251.88 | 82,837.93 |
| Year 6 | 82,837.93 | 6,931.82 | 4,556.09 | 2,375.74 | 80,462.19 |
| Year 7 | 80,462.19 | 6,931.82 | 4,425.42 | 2,506.40 | 77,955.79 |
| Year 8 | 77,955.79 | 6,931.82 | 4,287.57 | 2,644.25 | 75,311.54 |
| Year 9 | 75,311.54 | 6,931.82 | 4,142.13 | 2,789.69 | 72,521.85 |
| Year 10 | 72,521.85 | 6,931.82 | 3,988.70 | 2,943.12 | 69,578.73 |
| Year 11 | 69,578.73 | 6,931.82 | 3,826.83 | 3,104.99 | 66,473.74 |
| Year 12 | 66,473.74 | 6,931.82 | 3,656.06 | 3,275.77 | 63,197.97 |
| Year 13 | 63,197.97 | 6,931.82 | 3,475.89 | 3,455.93 | 59,742.04 |
| Year 14 | 59,742.04 | 6,931.82 | 3,285.81 | 3,646.01 | 56,096.03 |
| Year 15 | 56,096.03 | 6,931.82 | 3,085.28 | 3,846.54 | 52,249.48 |
| Year 16 | 52,249.48 | 6,931.82 | 2,873.72 | 4,058.10 | 48,191.38 |
| Year 17 | 48,191.38 | 6,931.82 | 2,650.53 | 4,281.30 | 43,910.09 |
| Year 18 | 43,910.09 | 6,931.82 | 2,415.05 | 4,516.77 | 39,393.32 |
| Year 19 | 39,393.32 | 6,931.82 | 2,166.63 | 4,765.19 | 34,628.13 |
| Year 20 | 34,628.13 | 6,931.82 | 1,904.55 | 5,027.28 | 29,600.85 |
| Year 21 | 29,600.85 | 6,931.82 | 1,628.05 | 5,303.78 | 24,297.08 |
| Year 22 | 24,297.08 | 6,931.82 | 1,336.34 | 5,595.48 | 18,701.60 |
| Year 23 | 18,701.60 | 6,931.82 | 1,028.59 | 5,903.23 | 12,798.36 |
| Year 24 | 12,798.36 | 6,931.82 | 703.91 | 6,227.91 | 6,570.45 |
| Year 25 | 6,570.45 | 6,931.82 | 361.37 | 6,570.45 | -0.00 |
| 80,312.56 |
| EMI | 5767.99 | PMT(9%,10,-17017) |
| Loan balance | 37017 | |
| interest rate | 9.00% | |
| Balance tenor | 10 |
| Year | Opening o/s (i) | EMI (ii) | Interest
(iii) [(i)*7.5%] |
Principal
(iv) [(ii)-(iii)] |
O/s
(v) [(i)-(iv)] |
| 1 | 37,017.00 | 5,767.99 | 3,331.53 | 2,436.46 | 34,580.54 |
| 2 | 34,580.54 | 5,767.99 | 3,112.25 | 2,655.74 | 31,924.79 |
| 3 | 31,924.79 | 5,767.99 | 2,873.23 | 2,894.76 | 29,030.03 |
| 4 | 29,030.03 | 5,767.99 | 2,612.70 | 3,155.29 | 25,874.74 |
| 5 | 25,874.74 | 5,767.99 | 2,328.73 | 3,439.27 | 22,435.48 |
| 6 | 22,435.48 | 5,767.99 | 2,019.19 | 3,748.80 | 18,686.68 |
| 7 | 18,686.68 | 5,767.99 | 1,681.80 | 4,086.19 | 14,600.49 |
| 8 | 14,600.49 | 5,767.99 | 1,314.04 | 4,453.95 | 10,146.54 |
| 9 | 10,146.54 | 5,767.99 | 913.19 | 4,854.80 | 5,291.74 |
| 10 | 5,291.74 | 5,767.99 | 476.26 | 5,291.74 | - |
| 20,662.92 |
Option 2 is recommended .Effective interest rate of combined mortgage = 80312.56+20662.92 = 100975.48
Interest rate = 100975.48/130000 = 78%
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