Final answer:
The rate of interest for the investment, with an initial amount of $597 and a final balance of $722.37 over three years, is approximately 6.63% per annum.
Step-by-step explanation:
To determine the rate of interest applied to an investment, where the final balance is $722.37 and the initial investment was $597 over three years, we can use the formula for compound interest. This formula is:
A = P(1 + r/n)^(nt)
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).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case, we need to solve for r, assuming the interest is compounded once per year (n = 1). Our equation becomes:
722.37 = 597(1 + r)^3
We solve for r:
(722.37 / 597) = (1 + r)^3
1.21005 = (1 + r)^3
To find r, we take the cube root of 1.21005:
(1.21005)^(1/3) = 1 + r
1.0663 (approximately) = 1 + r
r = 1.0663 - 1
r = 0.0663 or 6.63%
Therefore, the investment was made at an approximate annual interest rate of 6.63%.