Okay, let's walk through this step-by-step:
The initial balance of the savings account: $312.50
The final balance after 9 years: $1250
Let's call the interest rate r.
We know the final balance is the initial balance times (1 + r)^9
(because of continuous compounding over 9 years)
So:
312.50 = (1 + r)^9
312.50 / (1 + r)^9 = 1250
Solving for r:
(312.50 / 1250)^(1/9) = 1 + r
0.2504 = 1 + r
0.7596 = r
Converting to a percentage:
0.7596 * 100% = 75.96%
Rounding to the nearest whole percent: 76%
So the interest rate is 76%.
Does this make sense? Let me know if you have any other questions!