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

Studdy Solution

STEP 1

Assumptions
1. The formula given is the compound interest formula: M=P(1+i)n M = P(1 + i)^n
2. The principal amount P 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 .
M=P(1+i)n M = P(1 + i)^n

STEP 3

Substitute P=$240 P = \$240 , i=0.08 i = 0.08 , and n=2 n = 2 into the formula.
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

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

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

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

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