Question

I am planning to invest $1,000 at the end of each month to my daughters college (starting at the end of this month) fund that earns a 12% annual rate of return compunded montly. Assuming that she starts college in exactly 5 years and she will spend 4 years in college, how much tuition can she afford to pay at the beginning of each of her 4 years in college?

Answer 1

The annual investement can be calculated by the formula:

maturity value= monthly investment*({[1+i]ⁿ-1}/i)*(1+i)

where i=annual rate /12

n=no.of months

using the above formula

total maturity value after year 1 = 1000*({[1+0.01]¹²}-1)*(1+0.01)= $12809.33 here,i=0.12/12=0.01 and n=12

total maturity value after year 2 = 1000*({[1+0.01]²⁴}-1)*(1+0.01)= $27243.20 here n= 2 years = 24 months

total maturity value after year 3 = 1000*({[1+0.01]³⁶}-1)*(1+0.01)=$43507.65 here n=36months

total maturity value after year 4 = 1000*({[1+0.01]⁴⁸}-1)*(1+0.01)=$61834.83 here n=48 months

total maturity value after year 1 = 1000*({[1+0.01]⁶⁰}-1)*(1+0.01)=$82486.37 here n= 60 months.