How much would you need to deposit in an account each month in order to have $20,000 in the account in 7 years? Assume the account earns 2% interest.
To calculate the monthly deposit needed to accumulate $20,000 in 7 years with a 2% interest rate, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Number of Compounding Periods
In this case, the future value is $20,000, the present value is the monthly deposit we want to find, the interest rate is 2% (or 0.02 in decimal form), and the number of compounding periods is 7 years * 12 months = 84 months.
So, the formula becomes:
$20,000 = Monthly Deposit * (1 + 0.02)^84
Now, we can rearrange the formula to solve for the monthly deposit:
Monthly Deposit = $20,000 / (1 + 0.02)^84
Let's calculate this using a calculator or a spreadsheet:
Monthly Deposit = $20,000 / (1.02)^84
= $20,000 / (1.795856)
By evaluating the expression, we find:
Monthly Deposit ≈ $11,136.53
Therefore, to have $20,000 in the account in 7 years with a 2% interest rate, you would need to deposit approximately $11,136.53 each month.
Use the annuity/compound interest formula:
FV=A(R^n-1)/(R-1)
where
A=monthly deposit
R=1+interest/period=1+0.02/12
FV=future value = 20000
n=number of periods = 7*12
Solve for A, where