Final answer:
To find the equivalent interest rate compounded monthly, we can use the formula for compound interest. In this case, the interest rate compounded monthly is approximately 0.008273 or 0.8273%.
Step-by-step explanation:
To find the equivalent interest rate compounded monthly, we can use the formula for compound interest:
Compound interest = Principal (1 + Interest rate/n)^(nt) - Principal
Where:
- Principal is the initial amount of money
- Interest rate is the annual interest rate
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, we are given:
- Principal = $10,000
- Interest rate = ?
- n = 12 (compounded monthly)
- t = 10 years
Substituting these values into the formula, we get:
$10,000 = $10,000 (1 + Interest rate/12)^(12 * 10) - $10,000
Simplifying the equation, we can solve for the interest rate:
Interest rate = (10,000/10,000)^(1/(12 * 10)) - 1
Calculating this expression, we find that the interest rate compounded monthly is approximately 0.008273 or 0.8273%.