Question

I want the solution for both Q1 and Q2

By using appropriate annuity formula in Q1 with explanations and details please

Abdullah, who is age five.

Mr. Ahmad earns $95,000 per year, but with the rising costs of education, their past contribution efforts have left them short of their financial goals. To estimate the amount of money Ahmad’s need to begin putting away for future security, some general information was obtained by their financial planner. The couple felt that the amount of money they currently contribute to their saving account would be sufficient for their retirement needs. What they had not accounted for was Abdullah's education. Mr. Ahmad is a graduate of American University Dubai, a private university with an extremely high tuition fee of approximately $20,000 per year. Mrs. Ahmad graduated from the British University Dubai. The tuition expense there is only $2,500 per year. When Abdullah turns 18, the couple wishes to send him to either of these exceptional universities. They have a slight preference for the American University. The problem, however, is that with the rate at which tuition fee is increasing Ahmad is not sure they can raise enough money. To assist in the calculations, assume the tuition at both universities will increase at an annual rate of five per cent. Living expenses are currently estimated at $4,000 per year at both schools. This expense is expected to grow at only three per cent per year. Further assume Ahmad can deposit their money into a growth oriented Investment fund at Dubai International Capital, which has historically earned a 12 per cent return per annum (one per cent per month). The couple wishes to have a pre-determined monthly amount automatically drafted from their checking account. When Abdullah starts college they will slowly liquidate the account by making an annual payment to Abdullah to cover tuition and living expenses at the beginning of each year for the four years he will be in college. Questions:

1-How much money will Mr. & Mrs. Ahmad have to deposit per month to allow Abdullah to attend American University? How much money will have to be deposited per month to allow Abdullah to attend the British University? (HINT: To answer this question you need to consider the costs of ALL four years.)

2-What is the relationship between the amount that must be deposited monthly by the parents and the future increases in both tuition and living expenses?

Answer 1

1) Case (i) - to join Abdullah in American University.

Abdullah' s age is 5 years. He will attend the University when he turns 18, i.e., after completion of 12 years. His parents has to pay tuition fees in the beginning of 13th, 14th, 15th and 16th years.

Currently, tuition fee is $20000. The tuition fee is assumed to increase 5% annually and living expenses at 3% annually.

So, the tuition fees and living expenses in the beginning of 13th year = 20000*(1.05)¹² + 4000*1.03¹²= $41620.17

the tuition fees and living expenses in the beginning of 14th year = 20000*(1.05)¹³ + 4000*1.03¹³ = $43587.12

the tuition fees and living expenses in the beginning of 15th year = 20000*(1.05)¹⁴ + 4000*1.03¹⁴= $45648.99

the tuition fees and living expenses in the beginning of 16th year = 20000*(1.05)¹⁵ + 4000*1.03¹⁵ = $47810.43

Discounting the values at the rate earned from investment fund i.e., 12%, the present value of the tuition fees = (41620.17/1.12¹²)+(43587.12/1.12¹³)+(45648.99/1.12¹⁴)+(47810.43/1.12¹⁵)

=$38747.38

Formula for annuity A,

P.V. = A*( (1- (1/1+i)ⁿ)/i). Where n=12*12=144 and i = 0.01 (because savings should be done monthly)

38747.38= A* 76.14

A = $508.90

Therefore, Mr. Ahmad has to save $508.90 monthly in investment fund so as to pay tuition fees for American University after the end of 12 years.

Case (ii) - to join Abdullah in British University.

So, the tuition fees and living expenses in the beginning of 13th year = 2500*(1.05)¹² + 4000*1.03¹²= $10192.68

the tuition fees and living expenses in the beginning of 14th year = 2500*(1.05)¹³ + 4000*1.03¹³ = $10588.26

the tuition fees and living expenses in the beginning of 15th year = 2500*(1.05)¹⁴ + 4000*1.03¹⁴= $11000.19

the tuition fees and living expenses in the beginning of 16th year = 2500*(1.05)¹⁵ + 4000*1.03¹⁵ = $11429.19

Discounting the values at the rate earned from investment fund i.e., 12%, the present value of the tuition fees = (10192.68/1.12¹²)+(10588.26/1.12¹³)+(11000.19/1.12¹⁴)+(11429.19/1.12¹⁵)

=$9381.67

Formula for annuity A,

P.V. = A*( (1- (1/1+i)ⁿ)/i). Where n=12*12=144 and i = 0.01 (because savings should be done monthly)

9381.67 = A*76.14

A = $123.22

Therefore, Mr. Ahmad has to save $123.22 monthly in investment fund so as to pay tuition fees for British University after the end of 12 years.

2)The amount that is deposited should include future inflation to adjust for the increase in the tuition fees and living expenses.