Question

1. Mr. Knox is planning to deposit $100 per year for the next 18 years for his grandson’s birthday. If the account earns an annual rate of 5% and deposits are made at the end of the year, how much money will Mr. Knox’s grandson have in the account in 18 years for college? How much money will be in the account if Mr. Knox deposits the money at the beginning of the year?

Answer 1

Answer:

a. $2953.9

b. $2813.24

Explanation:

To calculate the future value of an annuity paid at the beginning of the period, you have:

$VF = A\left[\frac{(1+i)^{n+1} - (1+i)}{i}\right] = 100\left[\frac{(1.05)^{19} - (1.05)}{0.05}\right] = 2953.9$

To calculate the future value of an annuity paid at the end of the period, you have:

$VF = A\left[\frac{(1+i)^{n} - 1)}{i}\right] = 100\left[\frac{(1.05)^{18} - 1)}{0.05}\right] = 2813.24$

Mr. Knox will have $2953.9 at the end of the 18 years, if he pays $100 at the beginning of each year. On teh other hand, Mr Knox will have $2813.24 at the end of the 18 years, if he pays $100 at the end of each year.