Question

(Calculating annuity payments) The Knutson Corporation needs to save $15 million to retire a $15 million mortgage that matures in 10 years. To retire this mortgage, the company plans to put a fixed amount into an account at the end of each year for 10 years. The Knutson Corporation expects to earn 10 percent annually on the money in this account. What equal annual contribution must the firm make to this account to accumulate the $15 million by the end of 10 years?

Answer 1

Answer:

Ans. The equal annual amount that the firm must save to this account to accumulate the $15 million by the end of 10 years is $941,180.92

Explanation:

Hi, we have to use the following equation and solve for "A". The equation is as follows.

$FutureValue=\frac{A((1+r)^{n} -1)}{r}$

Where:

A= Annuity (amount of money to save every year)

r= interest rate (in our case, 10% annually)

n= Quantity of yearly savings (10 contributions at the end of each year)

Everything should look like this

$15,000,000=\frac{A((1+0.1)^{10} -1)}{0.1}$

$15,000,000=A(15.9374246)$

$\frac{15,000,000}{15.9374246} =A$

$A=941,180.92$

So, in order to accumulate $15 million in 10 years at a rate of 10% annually, Knutson Corporation must make 10 equal contributions of $941,180.92 every year, at the end of each year.

Best of luck.