#### You need $80,000 in 10 years. If you can earn 0.47% per month, how much will you have to deposit today?

**Final Answer:**

To have $80,000 in 10 years with a monthly interest rate of 0.47%, you will need to deposit approximately $49,105.55 today. This is calculated through the present value formula using future value, interest rate, and number of months. Understanding these components helps in determining how much to invest today for a future goal.

**Examples & Evidence:**

To find out how much you need to deposit today to have $80,000 in 10 years with an interest rate of 0.47% per month, we can use the future value formula for calculating present value (PV):

FV= PV×(1+r)^{n}

Where:

- FV is the future value ($80,000)
- PV is the present value (the amount you need to deposit today)
- r is the monthly interest rate (0.47% per month or 0.0047 as a decimal)
- n is the total number of periods (10 years × 12 months = 120 months)

To find PV, we rearrange the formula:

Now we can plug in the values:

Calculating $(1.0047)120$:

(1.0047) 120≈1.62889

Then,

Thus, you will need to deposit approximately $49,105.55 today to have $80,000 in 10 years, earning 0.47% interest per month.

**Explanation:**

For example, if you wanted to know how much to deposit to reach $100,000 instead in the same timeframe and with the same interest rate, you would simply replace the $80,000 in the calculation with $100,000 and follow the same steps to find the new present value needed.

The method used is based on the standard financial formula for calculating present value, which is commonly taught in financial mathematics courses.

**More Answers:**