Question

use compounded interest rate unless it explicitly requires using simple interest.

You want to have $1.5 million 30 years from now. How much must you deposit each year (starting at the end of year 1 and ending at the end of year 40) if you are certain you can earn 7% annual interest with annual compounding?

Answer 1

ANSWER: since there is confusion with regarding to the number of years 30 or 40 , i am solving for 1.5 million required after 30 years and 1.5 million after 40 years , please check your details again as i am solving for both the scenarios.

1) Future value = 1,500,000 (after 40 years)

n = 40 years

i = 7%

deposit each year = ?

deposit each year = future value(a/f,i,n)

deposit each year = 1,500,000(a/f,7%,40)

deposit each year = 1,500,000 * 0.00501

deposit each year = 7,515

so i need to deposit $7,515 each year for 40 years to get 1.5 million dollars

2) Future value = 1,500,000 (after 30 years)

n = 30 years

i = 7%

deposit each year = ?

deposit each year = future value(a/f,i,n)

deposit each year = 1,500,000(a/f,7%,30)

deposit each year = 1,500,000 * 0.0106

deposit each year = 15,900

so i need to deposit $15,900 each year for 30 years to get 1.5 million dollars

i have solved for both n = 40 years and when n = 30 years and so please check with your teacher whether n is 40 or 30 and appropriately you can choose the relevant answer.