Today is your birthday and you decide to start saving for college. You will begin college on your 18th birthday and will need $10,000 per year at the end of each of the next 4 years (after that 18th birthday - isn't it nice the college lets you pay at the end of the year!) You will make an identical deposit each year up to and including the year you begin college. All your money will earn 12% interest including the time you are in college. If a deposit of $4,780.42 will allow you to reach your goal (gee, I love this question!) - are you ready for this?! How old are you now? (note points will only be given for work shown - no pure guesses please).
We are given,
Annual college expense = $10,000
No of years in college = 4
Annual interest rate = 12%
We can calculate the Present value of saving in excel,
| Annual expense(pmt) | 10000 | |
| No of years | 4 | |
| Interest rate | 12% | |
| Present value | 30373.49 | (=PV(12%,4,-10000,0,0) |
Hence total value of savings required at beginning of college is $30,373.49.
Annual deposit = $4,780.42
Interest rate = 12%
No of years = ?
We can calculate it in excel,
| pmt | 4780.42 | |
| interest | 12% | |
| Future Value | 30373 | |
| No of years | 5.0005 | (=Nper(12%,4780.42,0,30373,0) |
Hence the no of year of saving is 5 year. He will start college when he is 18. So his current age is 13.
If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.
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