Final answer:
To have $10,000 in ten years in a bank account with 10% interest compounded annually, Devin needs to deposit approximately $3,855.43 initially.
Step-by-step explanation:
The question is about determining the initial deposit required to reach a future value of $10,000 in a savings account after ten years, with an interest rate of 10% compounded annually. To find this initial deposit, we will use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this scenario, we have A = $10,000, n = 1 (since the interest is compounded annually), r = 10% or 0.1, and t = 10 years. To solve for P, the formula rearranges to P = A / (1 + r/n)^(nt).
Therefore, the initial deposit that Devin needs to make is:
P = $10,000 / (1 + 0.1/1)^(1*10)
P = $10,000 / (1.1)^10
P = $10,000 / (1.1)^10
P = $10,000 / 2.5937
P = $3,855.43 (approximately)
Devin would need to deposit approximately $3,855.43 into his savings account today to have $10,000 in ten years with a 10% annual compounded interest rate.