Final answer:
To find out how much you need to deposit initially to achieve a future amount with compound interest, you can manipulate the compound interest formula. By applying this to an example with a 10% annual interest rate and a $10,000 target in ten years, you would need an initial deposit of approximately $3,855.43.
Step-by-step explanation:
To determine the initial deposit required to achieve a certain future value with compound interest, we can use the compound interest formula:
A = P (1 + r/n)(nt)
where:
- A = the future value of the investment/loan, including interest.
- P = the principal investment amount (initial deposit or loan amount).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the number of years the money is invested or borrowed for.
To solve for the principal P, we rearrange the formula:
P = A / (1 + r/n)(nt)
Using an example, if you want to have $10,000 in ten years in an account that pays 10% interest compounded annually, you would calculate:
P = $10,000 / (1 + 0.10/1)(1*10)
P = $10,000 / (1.10)10 ≈ $3,855.43
This demonstrates the power of starting to save early and allowing compound interest to work in your favor.