Question

Mark opened a savings account at his bank with a guaranteed annual interest rate of 5.0% for 5 years. If he deposits $10,000.00 to the account and the interest is compounded annually, the interest on the account is modeled by the function A = 10,000(1 + .05)t.

Answer 1

To have $10,000 in ten years in a bank account that pays 10% interest compounded annually, you need to initially deposit approximately $3,853.04.

Step-by-step explanation:

To find out how much money you need to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A represents the ending balance, P represents the principal (initial amount), r represents the interest rate as a decimal, n represents the number of times the interest is compounded per year, and t represents the number of years.

In this case, we are given that A = $10,000, r = 0.10, n = 1 (compounded annually), and t = 10. Let's plug these values into the formula: $10,000 = P(1 + 0.10/1)^(1×10).

Simplifying the equation, we get: $10,000 = P(1.10)^10. To find the value of P, we need to solve for it. Dividing both sides of the equation by (1.10)^10, we get: P = $10,000 / (1.10)^10. Plugging this expression into a calculator, we find that P is approximately $3,853.04.

Answer 2

Total = Principal * (1 + rate) ^ years
Total = 10,000.00 * (1.05)^5
Total = 10,000.00 * 1.2762815625
Total = 12,762.82