1. The formula I = (Prt)/100 gives the simple interest earned, in dollars, for a deposit of P dollars earning simple interest at a rate of r percent for t years. Jackson invested $7,500.00 for a period of 2 years in a new account that earned simple interest at a rate of 2.5 percent. There were no other transactions in the account. What was the total amount of interest earned by the account for the 2-year period?
Answer: C
The total amount of interest earned by the account for the 2-year period is $375.00.
To calculate the total interest earned on Jackson's investment, we can apply the formula I = (Prt)/100. Substituting P = 7500, r = 2.5, and t = 2 into the formula gives us I = (7500 * 2.5 * 2) / 100 = $375.00.
A) $150.00
This option represents an incorrect calculation of the interest earned. If we mistakenly calculated using a shorter time period or a different rate, we might arrive at this figure, but it does not reflect the correct application of the formula for the given time and rate.
B) $187.50
This option is also incorrect. It may arise from miscalculating the interest for a single year or incorrectly applying the interest rate. However, using the given values in the formula clearly shows that the interest earned is higher than this amount.
C) $375.00
This is the correct answer. Using the formula I = (Prt)/100 with the values provided (P = 7500, r = 2.5, t = 2) accurately results in an interest amount of $375.00. This option represents the correct application of the simple interest formula.
D) $750.00
This option is incorrect as it suggests a calculation that would imply either a higher interest rate or a longer duration than what was specified. The values provided lead to a lower total interest than this amount, making it an invalid choice.
Conclusion
The calculation of simple interest using the formula I = (Prt)/100 definitively shows that the total interest earned by Jackson's investment over 2 years at a rate of 2.5 percent is $375.00. All other options fail to correctly apply the formula or misinterpret the variables involved, confirming that C is the only valid answer.