How much must be deposited today into the following account in order to have $ 75 comma 000 in 5  years for a down payment on a​ house? Assume no additional deposits are made.
An account with monthly compounding and an APR of 6​%

To determine how much must be deposited today to reach a future value of $75,000 in 5 years with an annual percentage rate (APR) of 6%, compounded monthly, we can use the **Present Value formula for compound interest**:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ PV $ is the present value (the amount to deposit today)
- $ FV $ is the future value ($75,000)
- $ r $ is the annual interest rate (6% or 0.06)
- $ n $ is the number of times the interest is compounded per year (monthly compounding means $ n = 12 $)
- $ t $ is the number of years (5 years)

Let's calculate the present value (PV).The amount that must be deposited today to have $75,000 in 5 years, with a 6% APR compounded monthly, is approximately **$55,602.91**.

Do you want further details or have any questions?

Here are 5 related questions for further exploration:
1. What if the APR was 5% instead of 6%?
2. How would the required deposit change if the interest was compounded quarterly?
3. What if you wanted to save $100,000 instead of $75,000?
4. How does the present value change with an increase in the compounding frequency (e.g., daily)?
5. What happens to the required deposit if you extend the time period to 10 years?

**Tip:** The more frequent the compounding, the more interest you earn, but the effect is less pronounced with very frequent compounding.

How much must be deposited today into the following account in order to have $75,000 in 5 years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of 6%.

Learn how to calculate the amount that must be deposited today to have $75,000 in 5 years for a house down payment. This guide uses the present value formula with a 6% APR compounded monthly, suitable for college-level students.

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