Question

A student needs fees of 30000 per year, to be paid at the start of each year for 3 years. She will also need 5000 per month living expenses, starting now. Interest is calculated at 8% compounded monthly.

a) What is the effective interest rate?

b) How much capital must parents have to pay the fees?

c) How much capital must parents have to pay the living expenses? How much capital do the parents need altogether?

Answer 1

a)

Interest rate per month = 8%/12 = 0.67%

Effective interest rate = [(1 + 0.0067)^12 - 1] *100

= [(1.0067)^12 - 1]*100 = 1.08343 - 1 *100 = 8.343%

b)

Fees needed at the starting of each year = 30000

Maturity = 3 years

Capital required to pay the fees = 30000 + 30000*Present value annuity factor(8.343%,2)

= 30000 + 30000*1.7749

= 30000 + 53247 = 83247

c)

Fees needed per month at the beginning = 5000

Number of months fees required = 12*3 = 36 months

Interest rate per month = 0.67%

Capital required to pay the living expenses = 5000 + 5000*Present value annuity factor(0.67%,35)

= 5000 + 5000*31.106 = 5000 + 155530 = 160530

Capital required by parents = 83247 + 160530 = 243777