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Suppose you want to have $400,000 for retirement in 25 years. Your account earns 7% interest. How much would you need to deposit in the account each month to reach your goal?Round your answer to the nearest cent as needed.

Question

Suppose you want to have $400,000 for retirement in 25 years. Your account earns 7% interest. How much would you need to deposit in the account each month to reach your goal?Round your answer to the nearest cent as needed.

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Solution

To solve this problem, we can use the formula for the future value of a series of monthly payments or annuities:

FV = P * [(1 + r/n)^(nt) - 1] / (r/n)

where: FV = future value = $400,000 P = monthly payment (what we're trying to find) r = annual interest rate = 7% = 0.07 n = number of times the interest is compounded per year = 12 (since we're making monthly payments) t = number of years = 25

We can rearrange the formula to solve for P:

P = FV * (r/n) / [(1 + r/n)^(nt) - 1]

Substituting the given values:

P = 400,000 * (0.07/12) / [(1 + 0.07/12)^(12*25) - 1]

Now, we can calculate the value:

P = 400,000 * 0.00583333 / [(1 + 0.00583333)^(300) - 1] P = 2333.33 / [(1.00583333)^300 - 1] P = 2333.33 / [10.244507 - 1] P = 2333.33 / 9.244507 P = 252.39

So, you would need to deposit approximately 252.39eachmonthtoreachyourgoalof252.39 each month to reach your goal of 400,000 in 25 years with an annual interest rate of 7%.

This problem has been solved

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