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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.)
Found 2 solutions by ikleyn, CPhill:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
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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It is a classic Ordinary Annuity saving plan (assuming that the deposits are made at the end of each month).
The general formula is
FV =  ,
where FV is the future value of the account; P is the monthly payment (deposit);
r is the effective monthly compounding rate presented as a decimal;
n is the number of deposits (= the number of years multiplied by 12, in this case).
From this formula, you get for the monthly payment
P =  . (1)
Under the given conditions, FV = $20,000; r = 0.04/12; n = 6*12 = 72. So, according to the formula (1), you get
for the monthly payment
P =  = $246.24 (rounded).
Answer. The necessary monthly deposit value is $246.24.
Solved.
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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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To make such complicated calculations as they are in this problem,
you should have/use an appropriate calculator for such long formulas.
Ideal choice is MS Excel, or Google spreadsheets, if you have it in your computer.
Then you write a formula in a text editor, copy-paste it
into an Excel worksheet cell and click "enter" - the result is ready
in the next second.
If you have no MS Excel in your computer, you may find similar
free of charge online calculators in the Internet. One such calculator is
www.desmos.com/calculator
It allows you to do the same thing: you write a formula in a text editor,
copy-paste it into this calculator and click "enter" - the result is ready
in the next second.
Answer by CPhill(1959)  (Show Source):
You can put this solution on YOUR website! Here's how to calculate the monthly deposit amount:
**1. Convert Annual Interest Rate to Monthly Rate:**
* Annual interest rate: 4% = 0.04
* Monthly interest rate: 0.04 / 12 = 0.003333...
**2. Calculate the Total Number of Months:**
* Savings period: 6 years
* Total months: 6 years * 12 months/year = 72 months
**3. Use the Future Value of an Ordinary Annuity Formula (Solve for PMT):**
* FV = PMT * [((1 + r)^n - 1) / r]
* FV = Future Value ($20,000)
* PMT = Payment (monthly deposit)
* r = Monthly interest rate (0.003333...)
* n = Number of months (72)
* Rearrange the formula to solve for PMT:
* PMT = FV / [((1 + r)^n - 1) / r]
* PMT = FV * [r / ((1 + r)^n - 1)]
**4. Plug in the Values and Calculate:**
* PMT = 20000 * [0.003333 / ((1 + 0.003333)^72 - 1)]
* PMT ≈ $246.24
**Answer:** You would need to deposit approximately $246.24 each month.
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