Question

find the amount of time.

1. $i = $720, $p = $10000, $r = 9%$
2. $i = $450, $p = $2400, $r = 7.5%$

Explanation:

Problem 20:

Step1: Recall simple interest formula

The simple interest formula is \( I = P \times r \times t \), where \( I \) is interest, \( P \) is principal, \( r \) is rate (in decimal), and \( t \) is time. We need to solve for \( t \), so rearrange the formula: \( t=\frac{I}{P\times r} \).

Step2: Convert rate to decimal

Given \( r = 9\%=0.09 \), \( I = \$720 \), \( P=\$10000 \).

Step3: Substitute values into formula

Substitute \( I = 720 \), \( P = 10000 \), \( r = 0.09 \) into \( t=\frac{I}{P\times r} \):
\( t=\frac{720}{10000\times0.09} \)

Step4: Calculate denominator

First, calculate \( 10000\times0.09 = 900 \).

Step5: Calculate time

Then, \( t=\frac{720}{900}=0.8 \) (assuming time is in years, or the relevant unit). Wait, no, wait: \( 10000\times0.09 = 900 \), \( 720\div900 = 0.8 \)? Wait, no, maybe I made a mistake. Wait, \( 10000\times0.09 = 900 \), \( 720\div900 = 0.8 \)? Wait, no, let's recalculate: \( 720\div(10000\times0.09)=720\div900 = 0.8 \)? Wait, that seems low. Wait, maybe the rate is annual, so maybe the formula is correct. Wait, let's check again. \( I = P*r*t \), so \( t = I/(Pr) \). So \( 720/(100000.09)=720/900 = 0.8 \) years? Or maybe the rate is 9% per year, so 0.8 years is about 9.6 months. Alternatively, maybe I messed up the principal. Wait, the problem says \( P = \$10000 \), \( I = \$720 \), \( r = 9\% \). So yes, \( t = 720/(10000*0.09)= 0.8 \) years. Wait, but maybe the question expects time in years, so 0.8 years, or maybe the rate is 9% per annum, so that's correct.

Wait, no, wait, 100000.09 is 900, 720/900 is 0.8. So time is 0.8 years, or 8 tenths of a year, which is 9.6 months. But maybe the problem expects it in years, so 0.8, or maybe I made a mistake. Wait, let's check again. \( I = P*r*t \), so \( t = I/(Pr) \). So 720 divided by (10000*0.09) is 720/900 = 0.8. So that's correct.

Problem 22:

Step1: Recall simple interest formula

Again, use \( I = P \times r \times t \), solve for \( t \): \( t=\frac{I}{P\times r} \).

Step2: Convert rate to decimal

Given \( r = 7.5\% = 0.075 \), \( I = \$450 \), \( P = \$2400 \).

Step3: Substitute values into formula

Substitute \( I = 450 \), \( P = 2400 \), \( r = 0.075 \) into \( t=\frac{I}{P\times r} \):
\( t=\frac{450}{2400\times0.075} \)

Step4: Calculate denominator

First, calculate \( 2400\times0.075 = 180 \).

Step5: Calculate time

Then, \( t=\frac{450}{180}=2.5 \) (assuming time is in years, or the relevant unit).

Answer:

s:

• Problem 20: \( t = \boldsymbol{0.8} \) (units depend on context, e.g., years)
• Problem 22: \( t = \boldsymbol{2.5} \) (units depend on context, e.g., years)