Solved on Feb 08, 2024

Find the future cost of a CD after 12 years, given an inflation rate of $4.5 \%$ and a present cost of $\$ 12.95$ . Round the answer to the nearest cent.

STEP 1

Assumptions
1. The present cost of the CD is $12.95.
2. The annual inflation rate is 4.5%.
3. The time period for calculating the future cost is 12 years.
4. The inflation rate is compounded annually.

STEP 2

To find the future cost of the CD, we need to use the formula for compound interest, which is also applicable for calculating the effects of inflation on cost.
$Future\, Cost = Present\, Cost \times (1 + Inflation\, Rate)^{Number\, of\, Years}$

STEP 3

Convert the inflation rate from a percentage to a decimal.
$4.5\% = 0.045$

STEP 4

Plug in the values for the present cost, inflation rate, and number of years into the formula.
$Future\, Cost = \$12.95 \times (1 + 0.045)^{12}$

STEP 5

Calculate the value inside the parentheses.
$1 + 0.045 = 1.045$

STEP 6

Now raise this value to the power of 12 to account for the compounding over 12 years.
$(1.045)^{12}$

STEP 7

Calculate the value of $(1.045)^{12}$ using a calculator.
$(1.045)^{12} \approx 1.7341$

STEP 8

Now multiply the present cost of the CD by the calculated value to find the future cost.
$Future\, Cost = \$12.95 \times 1.7341$

STEP 9

Calculate the future cost.
$Future\, Cost \approx \$12.95 \times 1.7341 \approx \$22.456795$

STEP 10

Round the answer to the nearest cent.
$Future\, Cost \approx \$22.46$
The cost of the CD in 12 years, assuming an inflation rate of $4.5\%$ , if its present cost is $\$12.95$ , will be approximately $\$22.46$ .

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Find the future cost of a CD after 12 years, given an inflation rate of $4.5 \%$ and a present cost of $\$ 12.95$ . Round the answer to the nearest cent.

STEP 1

Assumptions
1. The present cost of the CD is $12.95.
2. The annual inflation rate is 4.5%.
3. The time period for calculating the future cost is 12 years.
4. The inflation rate is compounded annually.

STEP 2

To find the future cost of the CD, we need to use the formula for compound interest, which is also applicable for calculating the effects of inflation on cost.
$Future\, Cost = Present\, Cost \times (1 + Inflation\, Rate)^{Number\, of\, Years}$

STEP 3

Convert the inflation rate from a percentage to a decimal.
$4.5\% = 0.045$

STEP 4

Plug in the values for the present cost, inflation rate, and number of years into the formula.
$Future\, Cost = \$12.95 \times (1 + 0.045)^{12}$

STEP 5

Calculate the value inside the parentheses.
$1 + 0.045 = 1.045$

STEP 6

Now raise this value to the power of 12 to account for the compounding over 12 years.
$(1.045)^{12}$

STEP 7

Calculate the value of $(1.045)^{12}$ using a calculator.
$(1.045)^{12} \approx 1.7341$

STEP 8

Now multiply the present cost of the CD by the calculated value to find the future cost.
$Future\, Cost = \$12.95 \times 1.7341$

STEP 9

Calculate the future cost.
$Future\, Cost \approx \$12.95 \times 1.7341 \approx \$22.456795$

STEP 10

Round the answer to the nearest cent.
$Future\, Cost \approx \$22.46$
The cost of the CD in 12 years, assuming an inflation rate of $4.5\%$ , if its present cost is $\$12.95$ , will be approximately $\$22.46$ .

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Find the future cost of a CD after 12 years, given an inflation rate of 4.5%4.5 \%4.5% and a present cost of $12.95\$ 12.95$12.95. Round the answer to the nearest cent.

STEP 1

Assumptions1. The present cost of the CD is $12.95.2. The annual inflation rate is 4.5%.3. The time period for calculating the future cost is 12 years.4. The inflation rate is compounded annually.

STEP 2

STEP 3

Convert the inflation rate from a percentage to a decimal.4.5%=0.0454.5\% = 0.0454.5%=0.045

STEP 4

Plug in the values for the present cost, inflation rate, and number of years into the formula.Future Cost=$12.95×(1+0.045)12Future\, Cost = \$12.95 \times (1 + 0.045)^{12}FutureCost=$12.95×(1+0.045)12

STEP 5

Calculate the value inside the parentheses.1+0.045=1.0451 + 0.045 = 1.0451+0.045=1.045

STEP 6

Now raise this value to the power of 12 to account for the compounding over 12 years.(1.045)12(1.045)^{12}(1.045)12

STEP 7

Calculate the value of (1.045)12(1.045)^{12}(1.045)12 using a calculator.(1.045)12≈1.7341(1.045)^{12} \approx 1.7341(1.045)12≈1.7341

STEP 8

Now multiply the present cost of the CD by the calculated value to find the future cost.Future Cost=$12.95×1.7341Future\, Cost = \$12.95 \times 1.7341FutureCost=$12.95×1.7341

STEP 9

Calculate the future cost.Future Cost≈$12.95×1.7341≈$22.456795Future\, Cost \approx \$12.95 \times 1.7341 \approx \$22.456795FutureCost≈$12.95×1.7341≈$22.456795

STEP 10

Round the answer to the nearest cent.Future Cost≈$22.46Future\, Cost \approx \$22.46FutureCost≈$22.46The cost of the CD in 12 years, assuming an inflation rate of 4.5%4.5\%4.5%, if its present cost is $12.95\$12.95$12.95, will be approximately $22.46\$22.46$22.46.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the future cost of a CD after 12 years, given an inflation rate of $4.5 \%$ and a present cost of $\$ 12.95$ . Round the answer to the nearest cent.

Assumptions
1. The present cost of the CD is $12.95.
2. The annual inflation rate is 4.5%.
3. The time period for calculating the future cost is 12 years.
4. The inflation rate is compounded annually.

Convert the inflation rate from a percentage to a decimal.
$4.5\% = 0.045$

Plug in the values for the present cost, inflation rate, and number of years into the formula.
$Future\, Cost = \$12.95 \times (1 + 0.045)^{12}$

Calculate the value inside the parentheses.
$1 + 0.045 = 1.045$

Now raise this value to the power of 12 to account for the compounding over 12 years.
$(1.045)^{12}$

Calculate the value of $(1.045)^{12}$ using a calculator.
$(1.045)^{12} \approx 1.7341$

Now multiply the present cost of the CD by the calculated value to find the future cost.
$Future\, Cost = \$12.95 \times 1.7341$

Calculate the future cost.
$Future\, Cost \approx \$12.95 \times 1.7341 \approx \$22.456795$

Round the answer to the nearest cent.
$Future\, Cost \approx \$22.46$
The cost of the CD in 12 years, assuming an inflation rate of $4.5\%$ , if its present cost is $\$12.95$ , will be approximately $\$22.46$ .