Question

If you deposit $4500 at the end of each of the be 20 years into an account paying 9.7% interest how much money will you account in 20 years? How much will you have if you make deposits in 40 years?

payment=

future value=

annual rate=

periods=

Compounding=

MODE= end or beginning

Answer 1

(a)-The money in the account in 20 years

Payment (P) = $4,500 per year

Future value = $249,119.03

Annual rate (r)= 9.70% per year

Periods (n) = 20 Years

Compounding = Annual Compounding

Mode = End of the year

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r]

= $4,500 x [{(1 + 0.0970)²⁰ – 1} / 0.0970]

= $4,500 x [(6.369899 – 1) / 0.0970]

= $4,500 x [5.639899 / 0.0970]

= $4,500 x 55.359784

= $249,119.03

(b)-The money in the account in 40 years

Payment (P) = $4,500 per year

Future value = $1,835,982.10

Annual rate (r)= 9.70% per year

Periods (n) = 40 Years

Compounding = Annual Compounding

Mode = End of the year

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r]

= $4,500 x [{(1 + 0.0970)⁴⁰ – 1} / 0.0970]

= $4,500 x [(40.575614 – 1) / 0.0970]

= $4,500 x [39.575614 / 0.0970]

= $4,500 x 407.996023

= $1,835,982.10