Question

Charlie is putting his little sister through college. He estimates that between tuition and cost of living, she will need $30,000 per year for the next four years. Assume Charlie will make these payments yearly, starting one year from today. If the effective annual interest rate is 8%, find the present value of Charlie’s total college costs.

With Explanation please

Answer 1

Information given:

Cost - 30,000 per year

Time - 4 years

Rate - 8%

Present value = Payment / (1 + rate/100 ) ^ year

Using the above formula we can find the present value of the four payments:

Present value = 30,000 / ( 1 + 8/100 )^1 + 30,000 / ( 1 + 8/100 )^2 + 30,000 / ( 1 + 8/100 )^3 + 30,000 / ( 1 + 8/100 )^4

= 30,000 / 1.08^1 + 30,000 / 1.08^2 + 30,000 /1.08^3 + 30,000 /1.08^4

= 30,000 / 0.9259 + 30,000 / 0.85734 + 30,000 / 0.79383 + 30,000 /0.73503

= 27,777.778 + 25720.2 + 23815 + 22050.9

= 99,363.805$

Thus, the present value of Charlie's total cost is 99,363.805$

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