Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Calculate the cost of each item in 13 years, assuming an annual inflation rate of 11% (compounded annually). Round your answers to the nearest cent.

a) Phone bill: $40

b) Pair of shoes: $65

c) New suit: $350

d) Monthly rent: $625

Sagot :

GinnyAnswer
To determine the cost of each of the given items in 13 years, assuming an annual inflation rate of 11%, we can use the compound interest formula:
[tex]\[ \text{Future Value} = \text{Present Value} \times (1 + r)^t \][/tex]
where:
- \(\text{Future Value}\) is the amount we are looking to find.
- \(\text{Present Value}\) is the current cost of the item.
- \(r\) is the inflation rate expressed as a decimal (11% = 0.11).
- \(t\) is the number of years (13 years).

Let's go through the calculation step-by-step for each item:

1. Phone Bill:
- Present Value (PV) = $40
- Inflation rate (r) = 0.11
- Number of years (t) = 13

Applying the formula:
[tex]\[ \text{Future Value} = 40 \times (1 + 0.11)^{13} \][/tex]
[tex]\[ \text{Future Value} \approx 40 \times 3.883225 \][/tex]
[tex]\[ \text{Future Value} \approx 155.33 \][/tex]
Therefore, the future cost of the phone bill will be approximately $155.33.

2. Pair of Shoes:
- Present Value (PV) = $65
- Inflation rate (r) = 0.11
- Number of years (t) = 13

Applying the formula:
[tex]\[ \text{Future Value} = 65 \times (1 + 0.11)^{13} \][/tex]
[tex]\[ \text{Future Value} \approx 65 \times 3.883225 \][/tex]
[tex]\[ \text{Future Value} \approx 252.41 \][/tex]
Therefore, the future cost of the pair of shoes will be approximately $252.41.

3. New Suit:
- Present Value (PV) = $350
- Inflation rate (r) = 0.11
- Number of years (t) = 13

Applying the formula:
[tex]\[ \text{Future Value} = 350 \times (1 + 0.11)^{13} \][/tex]
[tex]\[ \text{Future Value} \approx 350 \times 3.883225 \][/tex]
[tex]\[ \text{Future Value} \approx 1359.15 \][/tex]
Therefore, the future cost of the new suit will be approximately $1359.15.

4. Monthly Rent:
- Present Value (PV) = $625
- Inflation rate (r) = 0.11
- Number of years (t) = 13

Applying the formula:
[tex]\[ \text{Future Value} = 625 \times (1 + 0.11)^{13} \][/tex]
[tex]\[ \text{Future Value} \approx 625 \times 3.883225 \][/tex]
[tex]\[ \text{Future Value} \approx 2427.05 \][/tex]
Therefore, the future cost of the monthly rent will be approximately $2427.05.

In summary, the costs in 13 years will be:
- Phone bill: $155.33
- Pair of shoes: $252.41
- New Suit: $1359.15
- Monthly Rent: $2427.05
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.