In order to accumulate enough money for a down payment on a​ house, a couple deposits $ 772 per month into an account paying 6 % compounded monthly. If payments are made at the end of each​ period, how much money will be in the account in 7 ​years?
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Part 1
What is the amount in the account after 7 ​years?
​$
  
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To determine the amount of money in the account after 7 years, we use the formula for the future value of an ordinary annuity, since the deposits are made at the end of each period. The formula is:

\[
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
\]

Where:
- $ FV $ is the future value (the amount in the account after 7 years)
- $ P $ is the monthly deposit amount ($772)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the total number of deposits (number of months)

Given:
- The annual interest rate is 6%, so the monthly interest rate is:
  \[
  r = \frac{6\%}{12} = 0.005
  \]
- The total number of months in 7 years is:
  \[
  n = 7 \times 12 = 84
  \]

Now we can plug these values into the formula:

\[
FV = 772 \times \left(\frac{(1 + 0.005)^{84} - 1}{0.005}\right)
\]

Let me calculate this for you.The amount of money in the account after 7 years will be approximately **$80,345.07**.

Would you like further details on this or have any questions?

Here are 5 related questions to explore further:
1. How would the future value change if the interest rate were compounded quarterly instead of monthly?
2. What if the couple increased their monthly deposit amount by $100? How much would the total be after 7 years?
3. What is the total interest earned over the 7 years?
4. How does changing the deposit period (e.g., weekly deposits instead of monthly) affect the future value?
5. What if the couple decided to deposit for 10 years instead of 7? What would be the final amount?

**Tip:** To maximize savings, always check how the compounding frequency (monthly, quarterly, etc.) impacts the growth of your money. The more frequently interest is compounded, the higher the returns.

In order to accumulate enough money for a down payment on a​ house, a couple deposits $772 per month into an account paying 6% compounded monthly. If payments are made at the end of each​ period, how much money will be in the account in 7 ​years?

Discover how much a couple will have in their account after 7 years of depositing $772 per month at a 6% interest rate compounded monthly. This problem involves the future value of an ordinary annuity and compound interest, using key financial formulas.

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