Question

Lucinda Diamanti is 10 years old today (August 15th) and while all she’s interested in is her new bike, her parents Mr. & Mrs. Diamanti are considering how they will pay for her college education beginning in 8 years. They decide to set up a meeting with their financial adviser Cindy Morgan to discuss an education savings plan. During the meeting, the Diamanti’s inform Cindy that they have $8,000 they can use to begin the savings plan, and from what they can determine, Lucinda will require 4 years to complete her undergraduate degree in molecular biology. Cindy consults a reputable college reference to see that tuition costs are currently estimated at $32,000 per year and are expected to grow at 4% each year for the foreseeable future. The Diamanti’s are concerned that they won’t have enough money and ask Cindy how to make sure they have enough to completely pay for Lucinda’s undergraduate education. The Diamanti’s inform Cindy that they want to make deposits into the education savings plan on an annual basis until Lucinda’s first year in college at which point they will stop making contributions. Cindy tells them they can earn 8% annual interest on their savings plan. Your job to answer the following two questions (You may assume there are 8 years between today and the beginning of Lucinda’s first day in college): Assuming the estimates on tuition costs are correct, how much money needs to be in the account when Lucinda begins college in 8 years to fund 4 years of college?

Answer 1

Calculation of Future Value of fund required

Years	Future Value Factor	Future Value ( 32000 x FVF )
8	1.37- - (1.04)8	43,794
9	1.42-- (1.04)9	45,546
10	1.48- - (1.04)10	47,368
11	1.54 - - (1.04)11	49,263

The value calculated above is required at the end 8^th, 9^th , 10^th and 11^th year respectively during under graduation of Lucinda.

Calculation of Money needs to be in Account at the end of 8^th Year when Education Start

Year	Future Value	PVF (1.08)-t	Present Value at the end of 8th Year
8	43,794	1.00	43794
9	45,546	0.926	42,172
10	47,368	0.857	40,610
11	49,263	0.794	39,107
Total			165,683

-So Therefore total money need to be in account when education starts 8 year after from today is $ 165,683.

It means total of $ 165,683 required to be accumulated through annual contribution in 8 years.

Interest factor for annuity where future value is known is i / (1+i)ⁿ -1

By putting the value in above formula we will get

Interest factor = 0.094

Hence Annual Contribution at the end of each year = Interest Factor x Future Value

Annual Contribution 165,683 x 0.094

Annual Contribution = 15,577

It is assumed that annual contribution made at the end of each year till 8 year.