Final answer:
The interest earned on $10,000 in two days at a 6% interest rate, compounded daily, is $3.29.
Step-by-step explanation:
To calculate the amount of interest earned on $10,000 in two days at an interest rate of 6%, compounded daily, we can use the formula A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the principal amount (initial deposit)
- r is the annual interest rate (as a decimal)
- n is the number of times interest is compounded per year
- t is the time in years
In this case, P = $10,000, r = 0.06, n = 365 (since interest is compounded daily), and t = 2/365 (since we want to calculate the interest over two days). Plugging in these values, we get:
A = 10000(1 + 0.06/365)^(365 * 2/365)
Simplifying this expression gives us:
A = 10000(1 + 0.00016438356)^(2)
A = 10000(1.00016438356)^2
A = 10000 * 1.00032877
A = 10003.29
Therefore, the interest earned on $10,000 in two days at an interest rate of 6%, compounded daily, is $3.29.