Math / Algebra

QuestionThe 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 $A=P(1+r t)$
Use these formulas to evaluate the amounts indicated below.
Let $P=\$ 6,800, r=6.7 \%$ , and $t=9$ years. Determine the interest, $I$ , at the end of 9 years for a simple interest loan. $\begin{array}{l} \text { Interest }=\$ \\ \text { dollars } \end{array}$
Let $P=\$ 5,100, r=12.3 \%$ , and $t=3$ years. Determine the total end amount, $A$ , at the end of 3 years for a simple interest loan.
End Amount = \\square$ dollars

Studdy Solution

STEP 1

1. The formula for simple interest is $I = P \cdot r \cdot t$ .
2. The formula for the end amount of a simple interest investment or loan is $A = P(1 + r \cdot t)$ .
3. For the first calculation, $P = \$6,800$ , $r = 6.7\%$ , and $t = 9$ years.
4. For the second calculation, $P = \$5,100$ , $r = 12.3\%$ , and $t = 3$ years.

STEP 2

1. Calculate the interest $I$ for the first scenario.
2. Calculate the total end amount $A$ for the second scenario.

STEP 3

Convert the interest rate from a percentage to a decimal for the first scenario.
$r = 6.7\% = 0.067$

STEP 4

Use the simple interest formula to calculate $I$ .
$I = P \cdot r \cdot t$ $I = 6800 \cdot 0.067 \cdot 9$

STEP 5

Calculate the product to find the interest.
$I = 6800 \cdot 0.067 \cdot 9 = 4107.6$
The interest at the end of 9 years is:
$\boxed{4107.6}$

STEP 6

Convert the interest rate from a percentage to a decimal for the second scenario.
$r = 12.3\% = 0.123$

STEP 7

Use the formula for the total end amount $A$ .
$A = P(1 + r \cdot t)$ $A = 5100(1 + 0.123 \cdot 3)$

STEP 8

Calculate the expression inside the parentheses.
$A = 5100(1 + 0.369)$ $A = 5100 \cdot 1.369$

STEP 9

Calculate the product to find the total end amount.
$A = 5100 \cdot 1.369 = 6981.9$
The total end amount at the end of 3 years is:
$\boxed{6981.9}$

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Studdy Solution

STEP 1

STEP 2

1. Calculate the interest $I$ for the first scenario.
2. Calculate the total end amount $A$ for the second scenario.

STEP 3

Convert the interest rate from a percentage to a decimal for the first scenario.
$r = 6.7\% = 0.067$

STEP 4

Use the simple interest formula to calculate $I$ .
$I = P \cdot r \cdot t$ $I = 6800 \cdot 0.067 \cdot 9$

STEP 5

Calculate the product to find the interest.
$I = 6800 \cdot 0.067 \cdot 9 = 4107.6$
The interest at the end of 9 years is:
$\boxed{4107.6}$

STEP 6

Convert the interest rate from a percentage to a decimal for the second scenario.
$r = 12.3\% = 0.123$

STEP 7

Use the formula for the total end amount $A$ .
$A = P(1 + r \cdot t)$ $A = 5100(1 + 0.123 \cdot 3)$

STEP 8

Calculate the expression inside the parentheses.
$A = 5100(1 + 0.369)$ $A = 5100 \cdot 1.369$

STEP 9

Calculate the product to find the total end amount.
$A = 5100 \cdot 1.369 = 6981.9$
The total end amount at the end of 3 years is:
$\boxed{6981.9}$

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Studdy Solution

STEP 1

STEP 2

1. Calculate the interest I I I for the first scenario.2. Calculate the total end amount A A A for the second scenario.

STEP 3

Convert the interest rate from a percentage to a decimal for the first scenario.r=6.7%=0.067 r = 6.7\% = 0.067 r=6.7%=0.067

STEP 4

Use the simple interest formula to calculate I I I.I=P⋅r⋅t I = P \cdot r \cdot t I=P⋅r⋅t I=6800⋅0.067⋅9 I = 6800 \cdot 0.067 \cdot 9 I=6800⋅0.067⋅9

STEP 5

Calculate the product to find the interest.I=6800⋅0.067⋅9=4107.6 I = 6800 \cdot 0.067 \cdot 9 = 4107.6 I=6800⋅0.067⋅9=4107.6The interest at the end of 9 years is:4107.6 \boxed{4107.6} 4107.6​

STEP 6

Convert the interest rate from a percentage to a decimal for the second scenario.r=12.3%=0.123 r = 12.3\% = 0.123 r=12.3%=0.123

STEP 7

Use the formula for the total end amount A A A.A=P(1+r⋅t) A = P(1 + r \cdot t) A=P(1+r⋅t) A=5100(1+0.123⋅3) A = 5100(1 + 0.123 \cdot 3) A=5100(1+0.123⋅3)

STEP 8

Calculate the expression inside the parentheses.A=5100(1+0.369) A = 5100(1 + 0.369) A=5100(1+0.369) A=5100⋅1.369 A = 5100 \cdot 1.369 A=5100⋅1.369

STEP 9

Calculate the product to find the total end amount.A=5100⋅1.369=6981.9 A = 5100 \cdot 1.369 = 6981.9 A=5100⋅1.369=6981.9The total end amount at the end of 3 years is:6981.9 \boxed{6981.9} 6981.9​

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1. Calculate the interest $I$ for the first scenario.
2. Calculate the total end amount $A$ for the second scenario.

Convert the interest rate from a percentage to a decimal for the first scenario.
$r = 6.7\% = 0.067$

Use the simple interest formula to calculate $I$ .
$I = P \cdot r \cdot t$ $I = 6800 \cdot 0.067 \cdot 9$

Calculate the product to find the interest.
$I = 6800 \cdot 0.067 \cdot 9 = 4107.6$
The interest at the end of 9 years is:
$\boxed{4107.6}$

Convert the interest rate from a percentage to a decimal for the second scenario.
$r = 12.3\% = 0.123$

Use the formula for the total end amount $A$ .
$A = P(1 + r \cdot t)$ $A = 5100(1 + 0.123 \cdot 3)$

Calculate the expression inside the parentheses.
$A = 5100(1 + 0.369)$ $A = 5100 \cdot 1.369$

Calculate the product to find the total end amount.
$A = 5100 \cdot 1.369 = 6981.9$
The total end amount at the end of 3 years is:
$\boxed{6981.9}$