Lucinda Diamanti is 10 years old today (August 15th) and while all she’s interes
ID: 2653767 • Letter: L
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? Round your answer to a whole number. (No $ signs, commas, or decimal points)
Explanation / Answer
Calculation of Future Value of Requirement of Fund
Year
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 8th, 9th , 10th and 11th year respectively during under graduation of Lucinda.
Calculation of Money needs to be in Account at the end of 8th Year when Education Starts
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
Therefore total money needs to be in accounts 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.
Year
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
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