Simple Interest Applications The interest of a simple interest investment or loan can be computed with the formula \[ I=P r t \] The end amount of a simple interest investment or loan can be computed with the formula \[ A=P(1+r t) \] The total percentage rate or total return of a simple interest investment or loan can be computed with the formula \[ q=r t \text { (written as a percent) or } q=\frac{\text { Interest }}{\text { Principal }} \cdot 100 \] Use these formulas to evaluate the amounts indicated below. Rebecca invests \( \$ 13,000 \) at a simple interest rate of \( 8 \% \) for 9 years. Determine the interest she will receive from her investment at the end of 9 years. Rebecca will receive \$ \( \square \) of interest at the end of 9 years. dollars Determine the total amount she will receive from her investment at the end of 9 years. Rebecca will receive a total of \( \$ \) \( \square \) at the end of 9 years. dollars Determine the total percentage rate her interest will earn from her investment at the end of 9 years. Rebecca's investment will earn a total of \( \square \) \% interest relative to her initial investment at the end of 9 years. percent
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To determine the interest Rebecca will receive at the end of 9 years, we can plug the values into the simple interest formula \( I = P r t \). Here, \( P = 13,000 \), \( r = 0.08 \) (which is 8% expressed as a decimal), and \( t = 9 \). Calculating this, we find the interest \( I = 13,000 \times 0.08 \times 9 = 9,360 \). So, Rebecca will receive \$9,360 of interest at the end of 9 years. Now, to find the total amount Rebecca will receive from her investment, we use the formula \( A = P(1 + rt) \). Plugging in, we get \( A = 13,000 \times (1 + 0.08 \times 9) = 13,000 \times (1 + 0.72) = 13,000 \times 1.72 = 22,360 \). Hence, Rebecca will receive a total of \$22,360 at the end of 9 years. Finally, the total percentage rate her interest will earn can be calculated with \( q = r t \) which gives \( q = 0.08 \times 9 = 0.72 \) or 72%. Therefore, Rebecca's investment will earn a total of 72% interest relative to her initial investment at the end of 9 years.
