You deposit $10,000 in an account earning 3% interest, compounded semi-monthly (twice a month). You plan to leave the account untouched for 25 years. How much interest will you earn over the 25 years?

To calculate the interest earned over 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount including interest
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

In this case:
P = $10,000
r = 3% = 0.03 (as a decimal)
n = 2 (since interest is compounded semi-monthly, there are 2 compounding periods in a month)
t = 25 years

Let's plug these values into the formula:

A = $10,000(1 + 0.03/2)^(2*25)

A = $10,000(1 + 0.015)^50

A = $10,000(1.015)^50

Using a calculator, raise 1.015 to the power of 50 and multiply the result by $10,000:

A ≈ $10,000(1.437058)

A ≈ $14,370.58

Now subtract the initial deposit of $10,000 from the final amount to find the interest earned:

Interest earned = $14,370.58 - $10,000

Interest earned ≈ $4,370.58

Therefore, you will earn approximately $4,370.58 in interest over the 25 years.

compounds 24 times a year

so r = .03/24 = 0.00125 per period

25 years = 25*24 = 600 periods

A = 10,000 * 1.00125^600

= 10,000 * 2.116008731

= $21,160.09