Question

Suppose you want to have $300,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit in the account each month?

Answer 1

Using the future value formula, it is found that you would need to deposit $272.95 in the account each month.

What is the future value formula?

It is given by:

$V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right]$

In which:

• P is the payment.

• n is the number of payments.

• r is the interest rate.

For this problem, considering that there are monthly compoundings, the parameters are:

r = 0.08/12 = 0.0067, V(n) = 300000, n = 25 x 12 = 300.

Hence we solve for P to find the monthly payment.

$V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right]$

$300000 = P\left[\frac{(1.0067)^{299}}{0.0067}\right]$

1099.12P = 300000

P  = 300000/1099.12

P = $272.95.

You would need to deposit $272.95 in the account each month.

More can be learned about the future value formula at brainly.com/question/24703884

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