regina deposits 3500 in a savings account that pays 7 1/2 % interest , compounded semiannually. how much interest does the account earn in the first 6 months?

3500 * .075/2

1400

To calculate the amount of interest earned in the first 6 months, we need to 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 times interest is compounded per year
t = time in years

Given:
P = $3500
r = 7.5% (expressed as 0.075)
n = 2 (semiannually compounded)
t = 0.5 years (6 months)

Substituting the values into the formula:

A = 3500(1 + 0.075/2)^(2 * 0.5)

Simplifying the formula:

A = 3500(1.0375)^(1)

Calculating the value inside the parentheses:

A = 3500(1.0375)

A = 3631.25

To find the interest earned, subtract the principal amount:

Interest = A - P

Interest = 3631.25 - 3500

Interest = $131.25

Therefore, the account earns $131.25 in interest in the first 6 months.

To calculate the interest earned by the savings account in the first 6 months, we can use the formula:

Interest = Principal * (1 + (interest rate / n))^(n * t) - Principal

Where:
- Principal is the initial deposit amount, which is $3500 in this case.
- Interest rate is given as 7 1/2 %, which can be converted to a decimal as 0.075.
- n is the number of times interest is compounded per year. In this case, it is compounded semiannually, so n = 2.
- t is the time in years, which for the first 6 months is 0.5 years.

Let's now substitute the values into the formula and calculate the interest:

Interest = 3500 * (1 + (0.075 / 2))^(2 * 0.5) - 3500

First, divide the interest rate by the number of times compounded per year:
0.075 / 2 = 0.0375

Next, calculate the value inside the parentheses:
1 + 0.0375 = 1.0375

Raise the value by the power of the number of times compounded per year multiplied by the time in years:
(1.0375)^(2 * 0.5) = 1.0193

Finally, calculate the interest earned:
3500 * (1.0193) - 3500 = 34.76

Therefore, the account earns $34.76 in interest during the first 6 months.