Question

Beginning one month after birth of their son, Noah, the Nelsons deposited $100 each month in an annuity for his college fund. The annuity earned interest at an average rate of 6.8% compounded monthly until his 18th birthday. What was the amount of Noah's college fund on his 18th birthday? Referring to question 4, how much interest did Noah's college fund earn in total on his 18th birthday?

Answer 1

$100 * (1 + 6.8%/12)^216 + $100*(1+6.8%/12)^215 + ... + $100*(1+6.8%/12)^1

Now note that

x + x^2 + x^3 + ... + x^N = x ( 1 + x + ... + x^(N-1) )

= x ( (x^N -1)/(x-1) )

Here, x = 1+6.8%1 = 1.00566666 and N = 216, so

$100 * ( 1.00566666 ( 1.00566666^216 -1) / 0.00566666 )

= $ 42398.33

The total interest earned is $42,398 - $21,600 = $20,798

Explanation:

The generic formula used in this compound interest calculator is V = P(1+r/n)^(nt)

V = the future value of the investment

P = the principal investment amount

r = the annual interest rate

n = the number of times that interest is compounded per year

t = the number of years the money is invested for