How much would you need to deposit in an account each month in order to have $20,000 in the account in 10 years? Assume the account earns 4% interest.
Question
How much would you need to deposit in an account each month in order to have $20,000 in the account in 10 years? Assume the account earns 4% interest.
Solution
To solve this problem, we need to use the formula for the future value of a series of payments, or an ordinary annuity. The formula is:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
where: FV = future value of the annuity P = annuity payment r = annual interest rate (in decimal form) n = number of times that interest is compounded per year t = time the money is invested for in years
We know that FV = $20,000, r = 4% or 0.04, n = 1 (assuming interest is compounded annually), and t = 10 years. We want to solve for P, the annuity payment.
Rearranging the formula to solve for P gives us:
P = FV * (r/n) / [(1 + r/n)^(nt) - 1]
Substituting the known values gives us:
P = $20,000 * (0.04/1) / [(1 + 0.04/1)^(1*10) - 1]
Calculating the right side of the equation gives us the monthly deposit needed to reach $20,000 in 10 years with an annual interest rate of 4%.
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