Question

b. Assuming that college costs continue to increase at 4% per year and that all her college savings are invested in an account paying 7% interest, what would be the amount of money that she will need to have available at age 18 to pay for all four years of her undergraduate education? (1.5 pt)

Answer 1

Answer:

savings is  $97107.29

Explanation:

given data

college costs increase = 4% per year

invested paying r = 7%

available age g =  18

solution

we consider here Current Fees per year = $12500

we get here future value for 18 year that is

future value = 12500 × $(1+0.04)^{18}$     ...............1

future value FV = $25322.71

and

present value of growing annuity find the four years college fee

so here

Total Money =  $(\frac{FV}{r-g})\times (1-(\frac{1+g}{1+r})^t)\times (1+r)$     ................2

so put here value

Total Money = $(\frac{25322}{0.07-0.04})\times (1-(\frac{1+0.04}{1+0.07})^4)\times (1+0.07)$

Total Money = 97107.288177

so that savings is  $97107.29