Imagine Homer Simpson actually invested the $200,000 he earned providing Mr. Burns entertainment 7 years ago at 9% annual interest and starts investing an additional $1,700 a year today at the beginning of each year for 15 years at the same 9% annual rate. How much money will Homer have 15 years from today?
a. If Homer invested $200,000 7 years ago at 9% annual interest rate what is the value of this investment 15 years from now?
b. If Homer invests and additional $1,700 a year at the beginning of each year for 15 years at the same 9% annual rate, what is the future value of this investment 15 years from now?
c. How much money will Homer have 15 years from now
Homer Simpson actually invested the $200,000
he earned providing Mr. Burns entertainment 7 years ago at 9% annual interest and starts investing an additional $1,700 a year today at the beginning of each year for 15 years at the same 9%
How much money will Homer have 15 years from today
First of all we will find 200,000 prasent value which he has invested 7 years back
Its Prasent Value now is $ 365,608
| Year | Beginning Balance |
Interest | Ending Balance |
| 1 | 200,000 | 18000 | 218,000 |
| 2 | 218,000.00 | 19620 | 237,620 |
| 3 | 237,620.00 | 21385.8 | 259,006 |
| 4 | 259,005.80 | 23310.522 | 282,316 |
| 5 | 282,316.32 | 25408.469 | 307,725 |
| 6 | 307,724.79 | 27695.231 | 335,420 |
| 7 | 335,420.02 | 30187.802 | 365,608 |
a. If Homer invested $200,000 7 years ago at 9% annual interest rate what is the value of this investment 15 years from now?
Answer : $ 728,496
Calculation for the above answer
| Year | Beginning Balance |
Interest | Ending Balance |
| 1 | 200,000 | 18000 | 218,000 |
| 2 | 218,000.00 | 19620 | 237,620 |
| 3 | 237,620.00 | 21385.8 | 259,006 |
| 4 | 259,005.80 | 23310.522 | 282,316 |
| 5 | 282,316.32 | 25408.469 | 307,725 |
| 6 | 307,724.79 | 27695.231 | 335,420 |
| 7 | 335,420.02 | 30187.802 | 365,608 |
| 8 | 365,607.82 | 32904.704 | 398,513 |
| 9 | 398,512.53 | 35866.128 | 434,379 |
| 10 | 434,378.66 | 39094.079 | 473,473 |
| 11 | 473,472.73 | 42612.546 | 516,085 |
| 12 | 516,085.28 | 46447.675 | 562,533 |
| 13 | 562,532.96 | 50627.966 | 613,161 |
| 14 | 613,160.92 | 55184.483 | 668,345 |
| 15 | 668,345.41 | 60151.086 | 728,496 |
b. If Homer invests and additional $1,700 a year at the beginning of each year for 15 years at the same 9% annual rate, what is the future value of this investment 15 years from now?
Now we will calculate How much money will Homer have 15 years from today
Answer : $ 1,386,127
Calculation for the above answer is as follow
| 0 | Beginning Balance |
Addition | Total | Interest@ 9% | Ending Balance |
| 1 | 365,608 | 1700 | 367,308 | 33057.72 | 400,366 |
| 2 | 400,365.72 | 1700 | 402,066 | 36185.9148 | 438,252 |
| 3 | 438,251.63 | 1700 | 439,952 | 39595.64713 | 479,547 |
| 4 | 479,547.28 | 1700 | 481,247 | 43312.25537 | 524,560 |
| 5 | 524,559.54 | 1700 | 526,260 | 47363.35836 | 573,623 |
| 6 | 573,622.90 | 1700 | 575,323 | 51779.06061 | 627,102 |
| 7 | 627,101.96 | 1700 | 628,802 | 56592.17606 | 685,394 |
| 8 | 685,394.13 | 1700 | 687,094 | 61838.47191 | 748,933 |
| 9 | 748,932.60 | 1700 | 750,633 | 67556.93438 | 818,190 |
| 10 | 818,189.54 | 1700 | 819,890 | 73790.05848 | 893,680 |
| 11 | 893,679.60 | 1700 | 895,380 | 80584.16374 | 975,964 |
| 12 | 975,963.76 | 1700 | 977,664 | 87989.73848 | 1,065,653 |
| 13 | 1,065,653.50 | 1700 | 1,067,353 | 96061.81494 | 1,163,415 |
| 14 | 1,163,415.31 | 1700 | 1,165,115 | 104860.3783 | 1,269,976 |
| 15 | 1,269,975.69 | 1700 | 1,271,676 | 114450.8123 | 1,386,127 |
c. How much money will Homer have 15 years from now?
He will have $ 1,386,127
