Question

deposit starts year 19

Calculate the value of FV's Investment Account as requested below Timing of investment Assumptions Yield % Amount Frenquency Notes $150 Monthly Beginning of period Mom and Dad monthly investments 0 Nana and Papa periodic investments 8% $1,000 deposited at the beginning of year 6, year 11 and year 16 1,000 Yearly Beginning of period 8% 2 Tuition and expenses per year at XYZ University Starting in Year 19 25,000 3 4 5 6 1. What is the value of FV's investment account at the end of 18 years including deposits from FV's parents and grandparents? 7 2. What is the value of FV's investment account at the end of 19 years assuming tuition and expenses were paid to XYZ University at the beginning of year 19? Assume Mom and Dad continue to make monthly investments per above. 9 3. What is the value of FV's investment account after paying tuition at the beginning sophomore year (ie, beginning of year 20)? 0 1 Hint: This is a multi part analysis. You will need to add the investments made by Nana and Papa to the value of FV's account at the beginning of the appropriate vears.

Answer 1

1. What is the value of FV's investment account at the end of 18 years including deposits from parents and grandparents?

Solution:

Step 1: Let us first calculate value of investment account of parents

Parents (Mom & Dad) deposits $150 at the beginning of every month for 18 years at yield of 8%.

Since there is series periodic payment at the beginning of the month this is annuity due.

To find the value of parents' investment account at the end of 18 years we have to find future value of annuity due at 8% interest rate for 18 years.

Formula for Future Value of Annuity Due =   

(1+i)") -1*(1 + i) C *

Where,

C = periodic deposits, i = interest rate , n= number of period

Since here deposits are made monthly i = $\frac{8}{12}$ % = 0.67% and n = 18 * 12 = 216

Putting it in the formula,

Future value of parent's investment account will be

150 , (1+ - 1.1+ Sਰ 1200

Solving this we will get Future value of parent's investment as $72,493.01

(Tip : to calculate the same in excel use the formula FV(interest rate , number of period , periodic deposit , 0,1), Here it would be FV(8/1200,216,150,0,1))

Step 1: Now we will calculate value of investment account of grand parents

Grandparents will make $1,000 deposit at the beginning of 6th, 11th & 16th year at 8% yield.

This means deposit made in the beginning of 6th year would earn 8% compounded interest for 13 years (i.e. 18-6+1)

Similarly deposit made in the beginning of 11th year would earn 8% compounded interest for 8 years (i.e. 18-11+1)

And, deposit made in the beginning of 16th year would earn 8% compounded interest for 3 years (i.e. 18-16+1)

Formula for calculating future value of a deposit = ,

A*(1+r)"

where A = amount deposited , r= interest rate and n= number of periods

Here, for deposit made in 6th year A= 1000 , r = 8% , n=13

Similarly, for deposit made in 11th year A= 1000 , r = 8% , n=8

And, for deposit made in 16th year A= 1000 , r = 8% , n=3

Therefore value of investment account of grandparents =

(1000 *(1+0.08} }+ (1000 + (1+0.08}$) + (1000 *(1+0.0853)

= 2719.62+1850.93+1259.71 = $5830.27

Therefore, Future value of grandparent's investment is $ 5,830.27

Solution is Total investment account including parent & grand parents $78,323.27 (i.e.72,493.01 + 5,830.27)

2. What is the value of FV's investment account at the end of 19th year assuming tuition fees were paid at the beginning of 19th year?

Investment account at the end of 18^th year = $78,323.27 (from part 1)

Tuition fees to be paid at the beginning of the 19^th year = $25,000

Amount left in Investment account after paying tuition fees = 78,323.27 - 25,000 = $53,323.27 (Lets call this prior period investment amount)

This amount will earn interest of 8% during the year since both parents’ & grandparents’ investment has same yield of 8%

Therefore, value of prior period investment amount at the end of 19^th year will be = $ 57,589.13

(53, 323.27*(1+0.08}]}

Also, the parents will keep on investing $150 per month during the 19^th year. Again using the future value of annuity due where C=150, i=0.67% and n=12 we can calculate the investment value of new investment

Therefore, Investment value of new investment =

OOTI Haven + 1)* 7– (Gak * +) * 051

= $1,879.94

Therefore value of investment account at the end of 19^th year =    value of prior period investment amount + Investment value of new investment

= $ 57589.13 + $1,879.94 = $ 59,469.07

Solution is value of investment account at the end of 19^th year $ 59,469.07

3. What is the value of FV's investment account after paying tuition fees at the beginning of 20th year?

Investment account at the end of 19^th year = $ 59,469.07

Tuition fees to be paid at the beginning of the 19^th year = $25,000

Amount left in Investment account after paying tuition fees = 59,469.07 +25,000 = $ 34,469.07