Question

Rita has an investment account which compounds interest annually at a rate of 5.2%. After 6 years, she has $4500 in the account. How much money did she initially place in the account?

Answer 1

Rita initially placed approximately $3384.29 in her investment account, which compounded annually at a rate of 5.2% to reach $4500 after 6 years.

Step-by-step explanation:

To determine how much money Rita initially placed in her investment account, we apply the formula for compound interest. The formula to find the principal (initial amount) P, given the future value A, the annual interest rate r (as a decimal), the number of times interest is compounded per year n, and the time t in years is:

A = P(1 + r/n)^(nt)

Since the interest is compounded annually, n is 1. We have A = $4500, r = 0.052 (5.2%), and t = 6 years. Plugging these values into the formula and solving for P gives:

4500 = P(1 + 0.052/1)^(1*6)

4500 = P(1.052)^6

To find P, we divide both sides by (1.052)^6:

P = 4500 / (1.052)^6

P ≈ $3384.29

Therefore, Rita initially placed approximately $3384.29 in her investment account.