Question

As part of your financial​ planning, you wish to purchase a new car

7

years from today. The car you wish to purchase costs

​$10,000

​today, and your research indicates that its price will increase by

2​%

to

4​%

per year over the next

7

years.

a.  Estimate the price of the car at the end of 7 years if inflation is​ (1) 2​% per year and​ (2) 4​% per year. b.  How much more expensive will the car be if the rate of inflation is 4​% rather than 2​%? c.  Estimate the price of the car if inflation is 2​% for the next 3 years and 4​% for 4 years after that.

Answer 1

Please upvote if you like it and feel free to ask your query in the comment section.

Summary

In the question,

It is given that:

Purchase Cost of Car Today = $10,000

& we wish to purchase the car after 7 years from today.

So,

For knowing the value of Car after 7 Years, We have to calculate the future value of Car

And the formula is

Where

r = Inflation rate

n = number of years

Solution

Part a.

(1) Price of Car at the end of 7 years if inflation is 2% per year.

Using the formula, we have

=> Future Value = $10,000 x (1 + 2%) ⁷

=> Future Value = $10,000 x (1 + 0.02) ⁷

=> Future Value = $10,000 x (1.02)⁷

=> Future Value = $10,000 x 1.148686

Answer

=> Future Value = $11,486.86

Price of Car at the end of 7 years if inflation is 2% per year is $11,486.86

2) Price of Car at the end of 7 years if inflation is 4% per year.

Using the formula, we have

=> Future Value = $10,000 x (1 + 4%) ⁷

=> Future Value = $10,000 x (1 + 0.04) ⁷

=> Future Value = $10,000 x (1.04)⁷

=> Future Value = $10,000 x 1.315932

Answer

=> Future Value = $13,159.32

Price of Car at the end of 7 years if inflation is 4% per year is $13,159.32

Part b.

In this part, we have to calculate that how much more expensive will the car be at inflation rate of 4% rather than 2%.

So,

The Car will be expensive by

= Price of Car after 7 years(at 4%) - Price of Car after 7 years (at 2%)

= $13,159.32 - $11,486.86      (As calculated in part a.)

= $1,672.46

Answer

The car is expensive by $1,672.46 if the inflation rate is 4% rather than 2%

Part c.

Now, In this part we have to calculate future value when inflation rate is not constant for each year.

So We will use the formula

Future Value = Present Value x (1 + r₁) x (1 + r₂) x (1 + r₃)x……….x (1 + r_n)

As the Interest rate is 2% for next 3 years and 4% for the remaining 4 years.

We have

Future Value = $10,000 (1 + 2%)(1+2%)(1+2%)(1+4%)(1+4%)(1+4%)(1+4%)

Future Value = $10,000 x 1.02 x 1.02 x 1.02 x 1.04 x 1.04 x 1.04 x 1.04

Future Value = $10,000 x 1.241463

Answer

Future Value = $12,414.63

Price of Car after 7 years at an inflation rate of 2% for 3 years and 4% for 4 years is $12,414.63

I hope it will help you in the study.

Please upvote if you like it and feel free to ask your query in the comment section.

Thank You!