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How much would you need to deposit in an account now in order to have $5000 in the account in 10 years? Assume the account earns 8% interest compounded monthly.

User Yangmei
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5 votes

Answer:

To calculate the amount you need to deposit now to have $5000 in the account in 10 years with an interest rate of 8% compounded monthly, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($5000)

P = the principal amount (the amount you need to deposit now)

r = the annual interest rate (8% or 0.08)

n = the number of times interest is compounded per year (12, since it's compounded monthly)

t = the number of years (10)

Let's solve the equation step by step:

1. Divide both sides of the equation by (1 + r/n)^(nt):

A / (1 + r/n)^(nt) = P

2. Substitute the given values into the equation:

5000 / (1 + 0.08/12)^(12*10) = P

3. Simplify the equation:

5000 / (1 + 0.00667)^(120) = P

4. Calculate the expression inside the parentheses:

5000 / (1.00667)^(120) = P

5. Evaluate the exponent:

5000 / (1.00667)^120 = P

6. Calculate the value inside the parentheses:

5000 / (1.95339628306) = P

7. Divide to find the principal amount:

P ≈ 2558.88

So, you would need to deposit approximately $2558.88 in the account now to have $5000 in the account in 10 years, assuming the account earns 8% interest compounded monthly.

Explanation:

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User RedPanda
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