4. Joe Levi bought a home in A
4. Joe Levi bought a home in Arlington, Texas, for $127,000. Heput down 25% and obtained a mortgage for 30 years at 8.00%. What isthe difference in interest cost if he had obtained a mortgage rateof 6.00%? (Use Table 15.1.) (Use 360 days a year. Round yourintermediate values and final answer to the nearest cent.)Difference $
Answer:
| Step-1: | Calculation of Interest costs at 8% | ||||||||||||
| a. | Monthly Payment | $ 699.18 | |||||||||||
| Working: | |||||||||||||
| i. | Present Value of annuity of 1 | = | (1-(1+i)^-n)/i | Where, | |||||||||
| = | (1-(1+0.00667)^-360)/0.00667 | i | 8%/12 | = | 0.00667 | ||||||||
| = | 136.2317 | n | 30*12 | = | 360 | ||||||||
| ii. | Cost of house | $ 1,27,000 | |||||||||||
| Down Payment | $ 31,750 | ||||||||||||
| Mortgage amount | $ 95,250 | ||||||||||||
| iii. | Monthly Payment | = | Mortgage Amount/Present value of annuity of 1 | ||||||||||
| = | $ 95,250 | / | 136.2317 | ||||||||||
| = | $ 699.18 | ||||||||||||
| b. | Total Interest costs | $ 1,56,453.50 | |||||||||||
| Working: | |||||||||||||
| Total Payment | = | $ 699.18 | x | 360 | = | $ 2,51,703.50 | |||||||
| Mortagage Amount | $ 95,250 | ||||||||||||
| Total Interest Costs | $ 1,56,453.50 | ||||||||||||
| Step-2: | Calculation of Interest costs at 6% | ||||||||||||
| a. | Monthly Payment | $ 571.07 | |||||||||||
| Working: | |||||||||||||
| i. | Present Value of annuity of 1 | = | (1-(1+i)^-n)/i | Where, | |||||||||
| = | (1-(1+0.005)^-360)/0.005 | i | 6%/12 | = | 0.005 | ||||||||
| = | 166.7916 | n | 30*12 | = | 360 | ||||||||
| ii. | Cost of house | $ 1,27,000 | |||||||||||
| Down Payment | $ 31,750 | ||||||||||||
| Mortgage amount | $ 95,250 | ||||||||||||
| iii. | Monthly Payment | = | Mortgage Amount/Present value of annuity of 1 | ||||||||||
| = | $ 95,250 | / | 166.7916 | ||||||||||
| = | $ 571.07 | ||||||||||||
| b. | Total Interest costs | $ 1,10,335.88 | |||||||||||
| Working: | |||||||||||||
| Total Payment | = | $ 571.07 | x | 360 | = | $ 2,05,585.88 | |||||||
| Mortagage Amount | $ 95,250 | ||||||||||||
| Total Interest Costs | $ 1,10,335.88 | ||||||||||||
| Step-3:Calculate difference in Interest Costs | |||||||||||||
| Interest Costs at 8% | $ 1,56,453.50 | ||||||||||||
| Interest Costs at 6% | $ 1,10,335.88 | ||||||||||||
| Difference in interest costs | $ 46,117.62 | ||||||||||||
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