Question

Rachel has a new-born daughter, Emma. She meets with her wealth manager at Fidelity to discuss a college fund for her daughter. The manager offers a plan that Rachel saves the same amount of money every year and then the fund will pay for Emma’s college education. Rachel forecasts that Emma will go to a four-year college at age 20, and each year’s college will cost $40000. If Rachel starts to save next year (at Emma’s age 1) and stops one year before Emma goes to college (at Emma’s age 19), and then the accumulated money in the fund will be exactly enough to pay for Emma’s four-year college education, how much would Rachel need to save today if Fidelity offers an interest rate of 10%? (Round to Integer)

(Hint 1: draw a timeline of cash flows based on Emma’s age.)

(Hint 2: you pay tuition each year

Answer 1

Solution :-

The Value of the College fees of Emma before 1 Year of start of college means at the Emma,s age of 19 years =

= $40,000 / ( 1 + 0.10 ) + $40,000 / ( 1 + 010 )² + $40,000 / ( 1 + 010 )³ + $40,000 / ( 1 + 010 )⁴

= ( $40,000 * 0.909 ) + ( $40,000 * 0.826 ) + ( $40,000 * 0.751 ) + ( $40,000 * 0.683 )

= $126,794.6

Now the Future value of amount deposit is equal to the present value of fees as per question

Rate of interest ( r ) = 10%

Time ( n ) = 19 Years

The Amount Paid every year = P

Future Value of Payment = ( FV ) =

A = $126.794.6 / 51.159

A = 2,478.44

= 2,479 ( Rounded ) for 19 Years

Rachel need to save every year $2,478.44 start one year from today

The Amount he need to save today to pay ever year amount = $126,794.6 / ( 1 + 0.10 )¹⁹

= $126,794.6 * 0.1635

= $20,731.93

If there is any doubt please ask in comments