To solve this problem, we’ll use the Present Value (PV) formula for compound interest:

$PV = \frac{FV}{(1 + \frac{r}{n})^{n \cdot t}}$

where:

• $FV$ is the future value (the target amount you want in the account, which is $5000).
• $r$ is the annual interest rate (7%, or 0.07).
• $n$ is the number of times interest is compounded per year (monthly, so $n = 12$).
• $t$ is the time in years (5 years).

Step-by-Step Solution

1. Substitute the given values into the formula:

$PV = \frac{5000}{(1 + \frac{0.07}{12})^{12 \cdot 5}}$

2. Calculate the monthly rate and exponent:

   • Monthly interest rate: $\frac{0.07}{12} = 0.0058333$
   • Total compounding periods: $12 \cdot 5 = 60$

3. Substitute these values to get:

$PV = \frac{5000}{(1 + 0.0058333)^{60}}$

4. Evaluate the expression inside the parentheses and the exponentiation, then divide.

Let me calculate this for you:

$PV \approx \frac{5000}{1.4166} \approx 3525.58$

Final Answer

To have $5000 in the account in 5 years at a 7% interest rate compounded monthly, you would need to deposit approximately $3525.58 now.

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

Related Questions

1. How much would you need to deposit for a goal of $10,000 in 10 years at 7% interest compounded monthly?
2. What would the required deposit be if the interest rate were 5% instead of 7%?
3. How does the result change if the interest compounds quarterly instead of monthly?
4. If the account compounds continuously, what initial deposit is required?
5. What is the effect of changing the time period to 3 years while keeping other values constant?

Tip

When calculating compound interest, breaking down the problem into smaller steps—like finding the monthly rate, periods, and exponent—can help avoid mistakes and make the process easier.