Final answer:
To find out how much money will be in your account after 22 years in an account with a 4.9% annual interest rate, use the compound interest formula: A = 118829(1 + 0.049)^22. The total amount after 22 years will be approximately $217,007.62.
Step-by-step explanation:
When you invest money in an account with a fixed interest rate, the amount of money grows over time due to compound interest. The initial amount, known as the principal, increases by a certain percentage every year. In the scenario given, you invest $118,829 at a 4.9% annual interest rate. To determine the total amount in the account after 22 years, we use the compound interest formula:
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.
For annual compounding, n = 1, so the formula simplifies to:
A = P(1 + r)^t
Using the given values, we calculate:
A = 118829(1 + 0.049)^22
After calculating, you find that the amount in the account after 22 years will be approximately $217,007.62.
This example emphasizes the power of compound interest and its capacity to grow investments significantly over time. It is evident why starting to save early and letting compound interest work can lead to substantial wealth accumulation, as noted in a second example where $3,000 grows to $44,923 in 40 years at a 7% annual return.