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?

how much interest did Noah’s college fund earn in total on his 18th birthday?

Guest Feb 26, 2021

#1**+1 **

SInce they put money in tha account at the beginning of the month....starting with month #2 , this is an 'Annuity due' calculation rather than an 'ordinary annuity'.....

FV = A [ ((1+i)^{n} -1 ) / i ] * (1 + i)

A = $ 100

i = interest per period in decimal form .068/12 (there are 12 periods per year...monthly)

n = number of periods = 18 * 12 - 1 (-1 because they did not deposit the first month)

= 215

A = 100 (1+.068/12)^{215 }/ (.068/12) * (1 + .068/12) = $ 59806.49

The interest will be this amount minus the amount they deposited which was 215 * 100

ElectricPavlov Feb 26, 2021