Solved on Dec 15, 2023

Calculate simple interest for given principal, rate, and time values.
$1000$ at $7\%$ for $3$ years $2500$ at $4.5\%$ for $30$ months $750$ at $2.8\%$ for $78$ weeks

STEP 1

Assumptions
1. The principle amounts are given as $1000,$ 2500, and $750 for the three different cases.<br />2. The interest rates are given as$ 7\% $,$ 4.5\% $, and$ 2.8\%$ for the three cases.
3. The time periods are given as 3 years, 30 months, and 78 weeks for the three cases.
4. The interest is calculated using the formula for simple interest, which is $ I = P \times R \times T $, where $ P $ is the principle, $ R $ is the rate (as a decimal), and $ T $ is the time in years.
5. We need to convert the time periods into years where necessary.

STEP 2

Convert the given interest rates from percentages to decimals by dividing by 100.
$7\% = \frac{7}{100} = 0.07$ $4.5\% = \frac{4.5}{100} = 0.045$ $2.8\% = \frac{2.8}{100} = 0.028$

STEP 3

Calculate the time in years for the second case, where the time is given in months.
$30\, months = \frac{30}{12}\, years$
$30\, months = 2.5\, years$

STEP 4

Calculate the time in years for the third case, where the time is given in weeks.
$78\, weeks = \frac{78}{52}\, years$
$78\, weeks = 1.5\, years$

STEP 5

Now, calculate the simple interest for the first case using the formula $I = P \times R \times T$ .
$I = 1000 \times 0.07 \times 3$

STEP 6

Compute the interest for the first case.
$I = 1000 \times 0.07 \times 3 = 210$

STEP 7

Now, calculate the simple interest for the second case using the formula $I = P \times R \times T$ .
$I = 2500 \times 0.045 \times 2.5$

STEP 8

Compute the interest for the second case.
$I = 2500 \times 0.045 \times 2.5 = 281.25$

STEP 9

Now, calculate the simple interest for the third case using the formula $I = P \times R \times T$ .
$I = 750 \times 0.028 \times 1.5$

STEP 10

Compute the interest for the third case.
$I = 750 \times 0.028 \times 1.5 = 31.5$

STEP 11

Complete the chart with the calculated interest values.
\begin{tabular}{|c|c|c|c|} \hline PRINCIPLE & RATE & TIME & I = Principle X Rate (as a decimal) X Time (in years) \\ \hline 1000 & $7 \%$ & 3 years & 210 \\ \hline 2500 & 4.5 \% & 30 months & 281.25 \\ \hline 750 & $2.8 \%$ & 78 weeks & $31.5 \\ \hline \end{tabular}

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Calculate simple interest for given principal, rate, and time values.
$1000$ at $7\%$ for $3$ years $2500$ at $4.5\%$ for $30$ months $750$ at $2.8\%$ for $78$ weeks

STEP 1

STEP 2

Convert the given interest rates from percentages to decimals by dividing by 100.
$7\% = \frac{7}{100} = 0.07$ $4.5\% = \frac{4.5}{100} = 0.045$ $2.8\% = \frac{2.8}{100} = 0.028$

STEP 3

Calculate the time in years for the second case, where the time is given in months.
$30\, months = \frac{30}{12}\, years$
$30\, months = 2.5\, years$

STEP 4

Calculate the time in years for the third case, where the time is given in weeks.
$78\, weeks = \frac{78}{52}\, years$
$78\, weeks = 1.5\, years$

STEP 5

Now, calculate the simple interest for the first case using the formula $I = P \times R \times T$ .
$I = 1000 \times 0.07 \times 3$

STEP 6

Compute the interest for the first case.
$I = 1000 \times 0.07 \times 3 = 210$

STEP 7

Now, calculate the simple interest for the second case using the formula $I = P \times R \times T$ .
$I = 2500 \times 0.045 \times 2.5$

STEP 8

Compute the interest for the second case.
$I = 2500 \times 0.045 \times 2.5 = 281.25$

STEP 9

Now, calculate the simple interest for the third case using the formula $I = P \times R \times T$ .
$I = 750 \times 0.028 \times 1.5$

STEP 10

Compute the interest for the third case.
$I = 750 \times 0.028 \times 1.5 = 31.5$

STEP 11

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Calculate simple interest for given principal, rate, and time values.100010001000 at 7%7\%7% for 333 years 250025002500 at 4.5%4.5\%4.5% for 303030 months 750750750 at 2.8%2.8\%2.8% for 787878 weeks

STEP 1

STEP 2

Convert the given interest rates from percentages to decimals by dividing by 100.7%=7100=0.077\% = \frac{7}{100} = 0.077%=1007​=0.07 4.5%=4.5100=0.0454.5\% = \frac{4.5}{100} = 0.0454.5%=1004.5​=0.045 2.8%=2.8100=0.0282.8\% = \frac{2.8}{100} = 0.0282.8%=1002.8​=0.028

STEP 3

Calculate the time in years for the second case, where the time is given in months.30 months=3012 years30\, months = \frac{30}{12}\, years30months=1230​years30 months=2.5 years30\, months = 2.5\, years30months=2.5years

STEP 4

Calculate the time in years for the third case, where the time is given in weeks.78 weeks=7852 years78\, weeks = \frac{78}{52}\, years78weeks=5278​years78 weeks=1.5 years78\, weeks = 1.5\, years78weeks=1.5years

STEP 5

Now, calculate the simple interest for the first case using the formula I=P×R×T I = P \times R \times T I=P×R×T.I=1000×0.07×3I = 1000 \times 0.07 \times 3I=1000×0.07×3

STEP 6

Compute the interest for the first case.I=1000×0.07×3=210I = 1000 \times 0.07 \times 3 = 210I=1000×0.07×3=210

STEP 7

Now, calculate the simple interest for the second case using the formula I=P×R×T I = P \times R \times T I=P×R×T.I=2500×0.045×2.5I = 2500 \times 0.045 \times 2.5I=2500×0.045×2.5

STEP 8

Compute the interest for the second case.I=2500×0.045×2.5=281.25I = 2500 \times 0.045 \times 2.5 = 281.25I=2500×0.045×2.5=281.25

STEP 9

Now, calculate the simple interest for the third case using the formula I=P×R×T I = P \times R \times T I=P×R×T.I=750×0.028×1.5I = 750 \times 0.028 \times 1.5I=750×0.028×1.5

STEP 10

Compute the interest for the third case.I=750×0.028×1.5=31.5I = 750 \times 0.028 \times 1.5 = 31.5I=750×0.028×1.5=31.5

STEP 11

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Calculate simple interest for given principal, rate, and time values.
$1000$ at $7\%$ for $3$ years $2500$ at $4.5\%$ for $30$ months $750$ at $2.8\%$ for $78$ weeks

Convert the given interest rates from percentages to decimals by dividing by 100.
$7\% = \frac{7}{100} = 0.07$ $4.5\% = \frac{4.5}{100} = 0.045$ $2.8\% = \frac{2.8}{100} = 0.028$

Calculate the time in years for the second case, where the time is given in months.
$30\, months = \frac{30}{12}\, years$
$30\, months = 2.5\, years$

Calculate the time in years for the third case, where the time is given in weeks.
$78\, weeks = \frac{78}{52}\, years$
$78\, weeks = 1.5\, years$

Now, calculate the simple interest for the first case using the formula $I = P \times R \times T$ .
$I = 1000 \times 0.07 \times 3$

Compute the interest for the first case.
$I = 1000 \times 0.07 \times 3 = 210$

Now, calculate the simple interest for the second case using the formula $I = P \times R \times T$ .
$I = 2500 \times 0.045 \times 2.5$

Compute the interest for the second case.
$I = 2500 \times 0.045 \times 2.5 = 281.25$

Now, calculate the simple interest for the third case using the formula $I = P \times R \times T$ .
$I = 750 \times 0.028 \times 1.5$

Compute the interest for the third case.
$I = 750 \times 0.028 \times 1.5 = 31.5$