Obrey will start attending college in September 2024 at which time she will need $10,000 for...

Obrey will start attending college in September 2024 at which time she will need $10,000 for the first year of study. Her costs at college for the next three years are estimated at $12,000, $13,000, and $14,000 respectively. Obrey’s family plans to make equal payments to a money market fund which yields 10%, the first payment will be paid in September 2012 and the last in September 2024. What is the size of the annual payments the family must make if the fund is to supply Obrey with the above estimates?

Expert Solution

Assuming today is Sept 2011

First let us calculate the PV (in Sept 2024) of all the college costs.

PV (2024) = 10,000 + 10,909.091 + 10,743.802 + 10,518.407 = $42,171.3

This is the amount that needs to be accumulated. So , we need to use the relation for Future value of Annuity. Remember the last annual payment in 2024 will already be at its future value.

n = (2023 - 2012) + 1 = 12 (Number of annuity payments. You can count them). The payment in 2024, as mentioned is already at its future value

r = 10%

We need to calculate P.

42,171.3 = P + 21.38P

P = $1,883.97

Hence, her family needs to make an annual payment of $1,883.97 starting nexy year (assuming today is Sept 2011)

P.S: Please let me know in comments if this assumption of today being Sept 2011 is not correct and what is the date today

jeff jeffy answered 2 years ago

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