Suppose you want to save $7,500 to go on a dream vacation in three years. You can save for your vacation by either depositing one single lump of money into a savings account and letting it accumulate interest or by making regular monthly payments. How much money, as a one-time deposit, PV , would you need to deposit into an account that earns 1.5% compounded monthly to earn a future value, FV , of $7,500 in three years? This amount can be found by using algebra to rearrange the function, FV=PV(1+rn)^(nY) , so that FV becomes an input variable and PV becomes the output variable. PV=FV(1+rn)^(−nY) Use this function to find the amount needed as a one-time deposit to earn $7,500 in 3 years. 
$7,500 will be enough money for your dream vacation in 3 years.

The interest rate for either account is 1.5% APR.

To calculate the amount needed for a one-time deposit (PV) to reach a future value (FV) of $7,500 in three years, we can use the formula:

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

Where:
- $FV = 7500$ (future value)
- $r = 0.015$ (annual interest rate, 1.5% as a decimal)
- $n = 12$ (compounding frequency per year, since it's compounded monthly)
- $Y = 3$ (number of years)

Let's calculate the present value (PV) needed.The amount of money you would need to deposit as a one-time lump sum to reach a future value of $7,500 in three years, with an interest rate of 1.5% compounded monthly, is approximately **$7,170.18**.

Would you like more details, or do you have any other questions?

Here are 5 related questions to explore:

1. How would the required lump sum change if the interest rate were higher, say 3%?
2. What if the interest was compounded quarterly instead of monthly?
3. How much would the future value be if you deposited $7,170.18 but kept it for 5 years?
4. How would making monthly payments instead of a lump sum affect the savings plan?
5. What would the one-time deposit be if the target amount was $10,000 instead of $7,500?

**Tip:** Compounding more frequently results in slightly higher future values for the same interest rate and time period.

Suppose you want to save $7,500 to go on a dream vacation in three years. You can save for your vacation by either depositing one single lump of money into a savings account and letting it accumulate interest or by making regular monthly payments. How much money, as a one-time deposit, PV, would you need to deposit into an account that earns 1.5% compounded monthly to earn a future value, FV, of $7,500 in three years?

Learn how to calculate the one-time deposit needed to save $7,500 for a dream vacation in 3 years with an interest rate of 1.5% compounded monthly. This problem demonstrates key concepts of algebra and compound interest. Suitable for high school students.

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