Question
In: Finance
Suppose you have a first job today, and you are planning to save 30% of your...
Suppose you have a first job today, and you are planning to save 30% of your annual wage at the end of the year. Your first-year annual wage will be $ 100,000 and it will grow by 3% per year. Assuming you work for 15 years in your first job, what is the present value of your saving for 15 years? The annual discount rate is given as 12%
I. $ 238,455.1 II. $ 230,164.7 III. $ 158,970 IV. $ 246,079.2
Solutions
Expert Solution
Annual wages is increasing by 3 % every year and saving is 30 % of the total wages for that year. Present value is calculated using present value factor at 12 % discount rate for that particular year.
The total present value of saving for 15 years at 12 % discount rate is $ 2,38,497 (approx) which is nearest to option 1.
The values are rounded off to nearest dollar, hence there the difference is due to rounding off. Correct option is 1.
This can be calculated as under -
| Year | Annual wage (in $) | savings per year (in $) | PVF (12%,n) | Present value of Savings |
| 1 | 1,00,000 | 30000 | 0.893 | 26790 |
| 2 | 103000 | 30900 | 0.797 | 24627 |
| 3 | 106090 | 31827 | 0.712 | 22661 |
| 4 | 109273 | 32781.9 | 0.636 | 20849 |
| 5 | 112551 | 33765.3 | 0.567 | 19145 |
| 6 | 115927 | 34778.1 | 0.507 | 17632 |
| 7 | 119405 | 35821.5 | 0.452 | 16191 |
| 8 | 122987 | 36896.1 | 0.404 | 14906 |
| 9 | 126677 | 38003.1 | 0.361 | 13719 |
| 10 | 130477 | 39143.1 | 0.322 | 12604 |
| 11 | 134392 | 40317.6 | 0.287 | 11571 |
| 12 | 138423 | 41526.9 | 0.257 | 10672 |
| 13 | 142576 | 42772.8 | 0.229 | 9795 |
| 14 | 146853 | 44055.9 | 0.205 | 9031 |
| 15 | 151259 | 45377.7 | 0.183 | 8304 |
| Total | 238497 |
Hope it helps !
jeff jeffy answered 2 years agoRelated Solutions
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