Question

Enn invests in a saving account with a fixed annual interest rate of 2.6% compounded monthly. After 25 years the account balance is $3024.43. How much was the initial investment?

Answer 1

The initial investment was approximately $916.51

Step-by-step explanation:

To find the initial investment, we need to use the formula for compound interest, given by: A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. In this case, we know that A = $3024.43, r = 2.6% = 0.026 (as a decimal), n = 12 (compounded monthly), and t = 25 years. Plugging these values into the formula, we get: $3024.43 = P(1 + 0.026/12)^(12*25). Now, we can solve for P by isolating it. First, divide both sides by (1 + 0.026/12)^(12*25). Then, divide both sides by (1 + 0.026/12)^(12*25) again to isolate P. Using a calculator, we find that the initial investment, P, is approximately $916.51.