SOLUTION: You deposit $200 each month into an account earning 7% interest compounded monthly. a) How much will you have in the account in 30 years? (Round down to the cents place.) b)

Question 1190655: You deposit $200 each month into an account earning 7% interest compounded monthly.
a) How much will you have in the account in 30 years? (Round down to the cents place.)
b) How much total money will you put into the account? (Give the exact value.)
c) How much total interest will you earn?
I am stuck on this; I've tried the formulas for it

Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to break down this compound interest problem:
**a) Future Value:**
We'll use the future value of an ordinary annuity formula:
FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value (what we want to find)
* P = Periodic payment ($200)
* r = Interest rate per period (7% annual / 12 months = 0.07/12 = 0.0058333...)
* n = Number of periods (30 years * 12 months = 360)
FV = 200 * [((1 + 0.0058333)^360 - 1) / 0.0058333]
FV = 200 * [ (7.612255 -1)/0.0058333]
FV = 200 * 1133.67
FV = 226734.14
Rounded down to the cents place, you'll have approximately **$226,734.14** in the account after 30 years.
**b) Total Money Deposited:**
This is a simple multiplication:
Total Deposited = Monthly Deposit * Number of Months
Total Deposited = $200 * 360
Total Deposited = **$72,000**
**c) Total Interest Earned:**
Total Interest = Future Value - Total Deposited
Total Interest = $226,734.14 - $72,000
Total Interest = **$154,734.14**

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
You deposit $200 each month into an account earning 7% interest compounded monthly.
a) How much will you have in the account in 30 years? (Round down to the cents place.)
b) How much total money will you put into the account? (Give the exact value.)
c) How much total interest will you earn?
I am stuck on this; I've tried the formulas for it
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Calculations in the post by @CPhill are not accurate.

The formula, which should be used is PV = . Calculations should be done without making intermediate rounding. Rounding is made at the end, ONLY. The correct answer to (a) is 243,994.20 dollars, which can be rounded to $243,994.

Solved.

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I used MS Excel in my computer, which works with 15 decimals after the decimal point,
providing a necessary precision.

It is equivalent to Google worksheet.

These are the best and the most appropriate calculators for such computing.

You write the formula in any text editor, copy-paste it into the spreadsheet cell and get the answer instantly.

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