Final answer:
To find the interest rate, we can use the formula for compound interest. Plugging in the given values and solving for r, we find that the interest rate is approximately 4.47%.
Step-by-step explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal amount
- r = annual interest rate (as a decimal)
- n = number of compounding periods per year
- t = number of years
In this case, we have:
- A = $3632
- P = $3000
- n = 1 (compounded annually)
- t = 7 years
Plugging in these values, we can solve for r:
$3632 = $3000(1 + r/1)^(1*7)
Dividing both sides by $3000 and taking the logarithm, we get:
log(3632/3000) = 7log(1 + r/1)
Simplifying, we find:
log(3632/3000) / 7 = log(1 + r)
Using a calculator to evaluate the logarithms, we find:
0.0449 = log(1 + r)
Converting back to exponential form, we get:
1 + r = 10^(0.0449)
Subtracting 1 and multiplying by 100, we find:
r = (10^(0.0449) - 1) * 100
Rounding to two decimal places, the interest rate is approximately 4.47%.