Blake Gray will finish high school in 7 years then wants to study a particular c
ID: 2630163 • Letter: B
Question
Blake Gray will finish high school in 7 years then wants to study a particular course at university which will take 4 years and cost $19 900 per year, paid at the start of each year. His parents want to pay for the course and they decide to start putting funds aside at a steady rate with the first payment today and continuing annually to the final year of the course. They will deposit the funds into an investment account that earns 4.49% per annum. (a) What is the present value of the university course fees?(b) How much money must his parents save each year starting from today?
Explanation / Answer
(a) What is the present value of the university course fees?
First payment is at the end of the 7th year from now (college first year start) = $19,900
Discounting it to now at 4.49% = 19,900/(1+0.0449)7 = $14632.885
Second payment is at the end of the 8th year from now (college second year start) = $19,900
Discounting it to now at 4.49% = 19,900/(1+0.0449)8 = $14004.10
Third payment is at the end of the 9th year from now (college third year start) = $19,900
Discounting it to now at 4.49% = 19,900/(1+0.0449)9 = $13402.34
Last payment is at the end of the 10th year from now (college fourth year start) = $19,900
Discounting it to now at 4.49% = 19,900/(1+0.0449)10 = $12826.43
Present value of course fees = $14632.885 + $14004.10 + $13402.34 + $12826.43 = $54865.76
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b) Payment period = 10 years
They are going to pay a fixed amount each year
PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]
= [(1+0.0449)10 - 1]/[0.0449 * (1+0.0449)10] = 7.92
PMT = payment per period
PV = PMT * PV interest rate factor
PV = $54865.76
54865.76 = PMT * 7.92
PMT = $6930.46
his parents must save $6930.46 each year starting from today
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