Question

​(Compound value​) The Aggarwal Corporation needs to save ​$13 million to retire a ​$13 million mortgage that matures in 13 years. To retire this​ mortgage, the company plans to put a fixed amount into an account at the end of each year for 13 ​years, with the first payment occurring at the end of 1 year. The Aggarwal Corporation expects to earn 13 percent annually on the money in this account. What equal annual contribution must it make to this account to accumulate the $ 13 million in 13 ​years? In order to retire a ​$13 million mortgage that matures in 13 ​years, what equal​ end-of-year contribution must the Aggarwal Corporation make to an account that earns 13 percent​ annually?

Answer 1

$433,550.11

Step-by-step explanation:

This is an ordinary annuity since the first payment occurs in 1 year. We can use the future value of an annuity formula to determine the annual contribution that must be made to the account.

future value = annual contribution x annuity factor

annual contribution = future value / annuity factor

• future value = $13,000,000
• FV annuity factor, 13%, 13 periods = 29.985

annual contribution = $13,000,000 / 29.985 = $433,550.11