Question

2. You need to have $150,000 for your children’s tuition. How much money do you need to set aside each month for this amount to be available in 15 years? a. If you were to invest the money in a savings account at 3% interest? b. If you were to invest the money in a bond fund at 6% interest? c. If you were to invest the money in an equity fund at 10% interest? d. What type of a problem is this?

Answer 1

Let P be the amount of money set at the beginning of each month for the next 15 years

Let r be the monthly rate of interest

The first P is compounded at r% for 15*12 = 180 months

The second P is compounded at r% for 179 months

There will be 180 P payments in total

The sum of future value of all these P payments = 150,000

.......equ1

(a) Investing in saving amount

interest rate = 3% pa

r: monthly interest rate

(1+r)^12 = (1+3%)^1

we get r = 0.2466%

Substituting this value of r in equ(1), we get

P = 661.38

(B) Investing in Bond

interest rate = 6% pa

r: monthly interest rate

(1+r)^12 = (1+6%)^1

we get r = 0.4868%

Substituting this value of r in equ(1), we get

P = 520.2760

(c) Investing in equity

interest rate = 10% pa

r: monthly interest rate

(1+r)^12 = (1+10%)^1

we get r = 0.7974%

Substituting this value of r in equ(1), we get

P = 373.4862

(d) This problem is of time value of money of an annuity and its senstivity with interest rate