Question

What amount would you have if you deposited $1,800 a year for 30 years at a 7 percent interest rate, compounded annually? Please round the discount factor to three decimal places and provide the final answer to the nearest whole dollar. Explain the calculations involved in determining the total amount accumulated over the given time period.

Answer 1

To determine the total amount accumulated over 30 years at a 7% interest rate, compounded annually, we can use the formula for compound interest. Plugging in the given values, the final amount accumulated is approximately $10,306.

Step-by-step explanation:

To determine the total amount accumulated over 30 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times compounding occurs in a year, and t is the number of years. In this case, P = $1,800, r = 7% = 0.07, n = 1 (compounded annually), and t = 30. Plugging in these values, the formula becomes:

A = 1800(1 + 0.07/1)^(1*30)

Using a calculator, we can evaluate the expression to find that A ≈ $10,305.69. Rounding this amount to the nearest whole dollar, the total amount accumulated over the 30-year period is approximately $10,306.