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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