Final answer:
To have $4000 in an account in 15 years with a 3% interest rate compounded monthly, you would need to deposit approximately $2349.53 now. This calculation uses the present value formula for compound interest, showing the powerful effect of compounding over time.
Step-by-step explanation:
The question asks us to calculate the present value (initial deposit) required to grow to $4000 after 15 years with an interest rate of 3%, compounded monthly. To solve this, we can use the formula for present value with compound interest:
PV = FV / (1 + r/n)(nt)
Where:
- PV = Present Value
- FV = Future Value ($4000)
- r = annual interest rate (0.03)
- n = number of times the interest is compounded per year (12)
- t = number of years (15)
Substituting the values we get:
PV = $4000 / (1 + 0.03/12)(12*15)
CV = $4000 / (1 + 0.0025)(180)
PV = $4000 / (1.0025)180
PV = $4000 / 1.702776
PV ≈ $2349.53
Therefore, you would need to deposit approximately $2349.53 in the account now to have $4000 in 15 years with the given interest rate.
Starting to save money early and using the power of compound interest can significantly increase your savings over time, as demonstrated by the example of saving $3,000 with a 7% annual rate to grow nearly fifteen-fold in 40 years.