Henry Hitchcock is 37 years old today and he wishes to accumulate $543,000 by his 58th...
Henry Hitchcock is 37 years old today and he wishes to accumulate $543,000 by his 58th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 37th through his 57th birthdays. What annual deposit must Henry make if the fund will earn 8% interest compounded annually?
Homework Answers
| Rate | Interest rate compounded annually | 8% | ||||||||
| Nper | Number of deposits | 21 | (58-37) | |||||||
| Fv | Future value required at 58th birthday | $543,000 | ||||||||
| Type | Deposits at beginning of years | 1 | ||||||||
| PMT | Annual deposit required from 37 to 57 birthday | $9,971.21 | (Using PMT function of excel with Rate=8%,Nper=37,Fv=-543000) | |||||||
| t | N=21-t | D | FV=D*(1.08^N) | |||||||
| Birthday | Year | Number of Years to future | Deposit | Future Value of Deposits | ||||||
| 37 | 0 | 21 | $9,971.21 | $50,193.44 | ||||||
| 38 | 1 | 20 | $9,971.21 | $46,475.40 | ||||||
| 39 | 2 | 19 | $9,971.21 | $43,032.78 | ||||||
| 40 | 3 | 18 | $9,971.21 | $39,845.17 | ||||||
| 41 | 4 | 17 | $9,971.21 | $36,893.67 | ||||||
| 42 | 5 | 16 | $9,971.21 | $34,160.81 | ||||||
| 43 | 6 | 15 | $9,971.21 | $31,630.38 | ||||||
| 44 | 7 | 14 | $9,971.21 | $29,287.39 | ||||||
| 45 | 8 | 13 | $9,971.21 | $27,117.95 | ||||||
| 46 | 9 | 12 | $9,971.21 | $25,109.21 | ||||||
| 47 | 10 | 11 | $9,971.21 | $23,249.27 | ||||||
| 48 | 11 | 10 | $9,971.21 | $21,527.10 | ||||||
| 49 | 12 | 9 | $9,971.21 | $19,932.50 | ||||||
| 50 | 13 | 8 | $9,971.21 | $18,456.02 | ||||||
| 51 | 14 | 7 | $9,971.21 | $17,088.91 | ||||||
| 52 | 15 | 6 | $9,971.21 | $15,823.06 | ||||||
| 53 | 16 | 5 | $9,971.21 | $14,650.99 | ||||||
| 54 | 17 | 4 | $9,971.21 | $13,565.73 | ||||||
| 55 | 18 | 3 | $9,971.21 | $12,560.86 | ||||||
| 56 | 19 | 2 | $9,971.21 | $11,630.42 | ||||||
| 57 | 20 | 1 | $9,971.21 | $10,768.91 | ||||||
| SUM | $543,000.00 | |||||||||
 |
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