Solved on Jan 25, 2024

Find the value of the variable $M$ in the formula $M=P(1+i)^{n}$ given that $P=\$ 240$ , $i=0.08$ , and $n=2$ . (Round to the nearest cent as needed.)

STEP 1

Assumptions
1. The formula given is the compound interest formula: $M = P(1 + i)^n$
2. The principal amount $P$ is $240
3. The interest rate per period $ i $ is 0.08
4. The number of periods $ n $ is 2
5. We need to find the value of $ M $, the amount after interest is applied

STEP 2

First, we will substitute the known values into the formula to find $M$ .
$M = P(1 + i)^n$

STEP 3

Substitute $P = \$240$ , $i = 0.08$ , and $n = 2$ into the formula.
$M = \$240(1 + 0.08)^2$

STEP 4

Calculate the value inside the parentheses.
$1 + 0.08 = 1.08$

STEP 5

Now raise 1.08 to the power of 2.
$(1.08)^2 = 1.08 \times 1.08$

STEP 6

Perform the multiplication to find the value of $(1.08)^2$ .
$(1.08)^2 = 1.1664$

STEP 7

Now multiply the principal amount $P$ by the result from the previous step to find $M$ .
$M = \$240 \times 1.1664$

STEP 8

Perform the multiplication to find the value of $M$ .
$M = \$240 \times 1.1664 = \$279.936$

STEP 9

Round the result to the nearest cent.
$M \approx \$279.94$
The value of $M$ after rounding to the nearest cent is \$279.94.

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Find the value of the variable $M$ in the formula $M=P(1+i)^{n}$ given that $P=\$ 240$ , $i=0.08$ , and $n=2$ . (Round to the nearest cent as needed.)

STEP 1

Assumptions
1. The formula given is the compound interest formula: $M = P(1 + i)^n$
2. The principal amount $P$ is $240
3. The interest rate per period \( i \) is 0.08
4. The number of periods \( n \) is 2
5. We need to find the value of \( M \), the amount after interest is applied

STEP 2

First, we will substitute the known values into the formula to find $M$ .
$M = P(1 + i)^n$

STEP 3

Substitute $P = \$240$ , $i = 0.08$ , and $n = 2$ into the formula.
$M = \$240(1 + 0.08)^2$

STEP 4

Calculate the value inside the parentheses.
$1 + 0.08 = 1.08$

STEP 5

Now raise 1.08 to the power of 2.
$(1.08)^2 = 1.08 \times 1.08$

STEP 6

Perform the multiplication to find the value of $(1.08)^2$ .
$(1.08)^2 = 1.1664$

STEP 7

Now multiply the principal amount $P$ by the result from the previous step to find $M$ .
$M = \$240 \times 1.1664$

STEP 8

Perform the multiplication to find the value of $M$ .
$M = \$240 \times 1.1664 = \$279.936$

STEP 9

Round the result to the nearest cent.
$M \approx \$279.94$
The value of $M$ after rounding to the nearest cent is \$279.94.

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Find the value of the variable MMM in the formula M=P(1+i)nM=P(1+i)^{n}M=P(1+i)n given that P=$240P=\$ 240P=$240, i=0.08i=0.08i=0.08, and n=2n=2n=2. (Round to the nearest cent as needed.)

STEP 1

Assumptions1. The formula given is the compound interest formula: M=P(1+i)n M = P(1 + i)^n M=P(1+i)n2. The principal amount P P P is $2403. The interest rate per period \( i \) is 0.084. The number of periods \( n \) is 25. We need to find the value of \( M \), the amount after interest is applied

STEP 2

First, we will substitute the known values into the formula to find M M M.M=P(1+i)n M = P(1 + i)^n M=P(1+i)n

STEP 3

Substitute P=$240 P = \$240 P=$240, i=0.08 i = 0.08 i=0.08, and n=2 n = 2 n=2 into the formula.M=$240(1+0.08)2 M = \$240(1 + 0.08)^2 M=$240(1+0.08)2

STEP 4

Calculate the value inside the parentheses.1+0.08=1.08 1 + 0.08 = 1.08 1+0.08=1.08

STEP 5

Now raise 1.08 to the power of 2.(1.08)2=1.08×1.08 (1.08)^2 = 1.08 \times 1.08 (1.08)2=1.08×1.08

STEP 6

Perform the multiplication to find the value of (1.08)2 (1.08)^2 (1.08)2.(1.08)2=1.1664 (1.08)^2 = 1.1664 (1.08)2=1.1664

STEP 7

Now multiply the principal amount P P P by the result from the previous step to find M M M.M=$240×1.1664 M = \$240 \times 1.1664 M=$240×1.1664

STEP 8

Perform the multiplication to find the value of M M M.M=$240×1.1664=$279.936 M = \$240 \times 1.1664 = \$279.936 M=$240×1.1664=$279.936

STEP 9

Round the result to the nearest cent.M≈$279.94 M \approx \$279.94 M≈$279.94The value of M M M after rounding to the nearest cent is \$279.94.

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Find the value of the variable $M$ in the formula $M=P(1+i)^{n}$ given that $P=\$ 240$ , $i=0.08$ , and $n=2$ . (Round to the nearest cent as needed.)

Assumptions
1. The formula given is the compound interest formula: $M = P(1 + i)^n$
2. The principal amount $P$ is $240
3. The interest rate per period \( i \) is 0.08
4. The number of periods \( n \) is 2
5. We need to find the value of \( M \), the amount after interest is applied

First, we will substitute the known values into the formula to find $M$ .
$M = P(1 + i)^n$

Substitute $P = \$240$ , $i = 0.08$ , and $n = 2$ into the formula.
$M = \$240(1 + 0.08)^2$

Calculate the value inside the parentheses.
$1 + 0.08 = 1.08$

Now raise 1.08 to the power of 2.
$(1.08)^2 = 1.08 \times 1.08$

Perform the multiplication to find the value of $(1.08)^2$ .
$(1.08)^2 = 1.1664$

Now multiply the principal amount $P$ by the result from the previous step to find $M$ .
$M = \$240 \times 1.1664$

Perform the multiplication to find the value of $M$ .
$M = \$240 \times 1.1664 = \$279.936$

Round the result to the nearest cent.
$M \approx \$279.94$
The value of $M$ after rounding to the nearest cent is \$279.94.