Final answer:
To find the ending balance of a $2,000 deposit with a 3.2% continuously compounded interest rate after 6 years, use the formula A = Pe^(rt). With e^(0.032*6) calculated, the ending balance is approximately $2,423.06.
Step-by-step explanation:
If you deposit $2,000 at 3.2% interest, compounded continuously, you can calculate the ending balance after 6 years using the formula for continuous compounding, which is: A = Pert, 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).
- t is the time the money is invested or borrowed for, in years.
- e is the base of the natural logarithm, approximately equal to 2.71828.
In this case, P = $2,000, r = 0.032 (which is 3.2% expressed as a decimal), and t = 6. So, the equation will look as follows:
A = 2000 * e(0.032 * 6)
You can use a calculator to find e raised to the power of (0.032x6). Once you find this value, multiply it by $2,000 to get your ending balance:
A ≈ 2000 * e0.192
A ≈ 2000 * 1.211527658
Therefore, the balance after 6 years would be roughly $2,423.06 to the nearest cent.