SOLUTION: How much would you need to deposit in an account each month in order to have $50,000 in the account in 7 years? Assume the account earns 6% interest.
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Question 1191376: How much would you need to deposit in an account each month in order to have $50,000 in the account in 7 years? Assume the account earns 6% interest. Found 2 solutions by CPhill, ikleyn:Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to figure out the monthly deposit you'd need:
**1. Understand the Problem**
This is a future value of an ordinary annuity problem. We need to find the regular payment (monthly deposit) that will result in a specific future value ($50,000) given an interest rate (6%) and a time period (7 years).
**2. Use the Formula**
The future value of an ordinary annuity formula is:
FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value ($50,000)
* P = Periodic Payment (what we want to find)
* r = Interest rate per period (6% annual rate / 12 months = 0.06/12 = 0.005)
* n = Number of periods (7 years * 12 months = 84)
**3. Solve for P**
We need to rearrange the formula to solve for the periodic payment (P):
P = FV * [r / ((1 + r)^n - 1)]
**4. Plug in the Values and Calculate**
P = $50,000 * [0.005 / ((1 + 0.005)^84 - 1)]
P = $50,000 * [0.005 / (1.517 - 1)]
P = $50,000 * [0.005 / 0.517]
P ≈ $483.37
**Answer:** You would need to deposit approximately $483.37 each month to have $50,000 in the account after 7 years.
