Sue bought a six-month CD for $ 30003000 She said that at maturity it paid $ 128128 in interest. Assume this was simple interest, and determine the APR.
I = PRT
128,128 = 30,003,000 * R * 0.5
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To calculate the Annual Percentage Rate (APR), we need to use the formula:
APR = (Interest / Principal) / Time
Where:
Interest is the amount of interest earned
Principal is the initial amount invested
Time is the period of time the investment was made in years
Given:
Principal (P) = $3000
Interest (I) = $128
Time (T) = 6 months = 0.5 years
Substituting the values into the formula:
APR = ($128 / $3000) / 0.5
Simplifying:
APR = 0.0426
To express this as a percentage, we multiply by 100:
APR = 4.26%
Therefore, the Annual Percentage Rate (APR) is 4.26%.
To determine the APR (Annual Percentage Rate), we need to calculate the interest rate per year that corresponds to the simple interest earned over six months.
The formula for calculating simple interest is:
Interest = Principal * Rate * Time
Given that Sue invested $3000 in a six-month CD and earned $128 in interest, we can plug these values into the formula to solve for the rate. The equation becomes:
128 = 3000 * Rate * 0.5
Simplifying the equation further:
Rate = 128 / (3000 * 0.5)
Rate = 128 / 1500
Rate = 0.0853 or 8.53%
Therefore, the Annual Percentage Rate (APR) for this six-month CD is 8.53%.