document.write( "Question 1209861: How much would you need to deposit in an account each month in order to have $20,000 in the account in 6 years? Assume the account earns 4% annual interest, compounded monthly. (Enter your answer to 2 decimal places.)
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Algebra.Com's Answer #850905 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Here's how to calculate the monthly deposit amount:\r
\n" ); document.write( "\n" ); document.write( "**1. Convert Annual Interest Rate to Monthly Rate:**\r
\n" ); document.write( "\n" ); document.write( "* Annual interest rate: 4% = 0.04
\n" ); document.write( "* Monthly interest rate: 0.04 / 12 = 0.003333...\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the Total Number of Months:**\r
\n" ); document.write( "\n" ); document.write( "* Savings period: 6 years
\n" ); document.write( "* Total months: 6 years * 12 months/year = 72 months\r
\n" ); document.write( "\n" ); document.write( "**3. Use the Future Value of an Ordinary Annuity Formula (Solve for PMT):**\r
\n" ); document.write( "\n" ); document.write( "* FV = PMT * [((1 + r)^n - 1) / r]
\n" ); document.write( " * FV = Future Value ($20,000)
\n" ); document.write( " * PMT = Payment (monthly deposit)
\n" ); document.write( " * r = Monthly interest rate (0.003333...)
\n" ); document.write( " * n = Number of months (72)\r
\n" ); document.write( "\n" ); document.write( "* Rearrange the formula to solve for PMT:
\n" ); document.write( " * PMT = FV / [((1 + r)^n - 1) / r]
\n" ); document.write( " * PMT = FV * [r / ((1 + r)^n - 1)]\r
\n" ); document.write( "\n" ); document.write( "**4. Plug in the Values and Calculate:**\r
\n" ); document.write( "\n" ); document.write( "* PMT = 20000 * [0.003333 / ((1 + 0.003333)^72 - 1)]
\n" ); document.write( "* PMT ≈ $246.24\r
\n" ); document.write( "\n" ); document.write( "**Answer:** You would need to deposit approximately $246.24 each month.
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