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As part of your financial planning, you wish to purchase a new car exactly 5 yea

ID: 2725342 • Letter: A

Question

As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs $14,000 today, and your research indicates that its price will increase by 2% to 4% per year over the next 5 years.

A) Estimate the price of the car at the end of 5 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 2 years and 4% for 3 years after that.

Explanation / Answer

Price of car Today = $14,000

A

1. If inflation rate = 2%

Price of car after 5 year = $14,000 × (1 + 2%) ^5

                                       = $14,000 × 1.104080

                                       = $15,457.13

Hence, Price of car if inflation rate is 2% is $15,457.13.

2. If inflation rate = 4%

Price of car after 5 year = $14,000 × (1 + 4%) ^5

                                       = $14,000 × 1.2167

                                       = $17,033.14

Hence, Price of car if inflation rate is 4% is $17,233.14.

B.

Different between price of car when inflation rate is 4% and 2% is calculated below:

Difference = $17,233.14 - $15,457.13

                  = $1,576.01

Hence, if inflation rate is 4% then car will $1,576.01 more expensive than inflation rate of 2%.

C,

If inflation rate is 2% for first 2 year and 4% for next three year then price of car is calculated below:

Price of car after 5 year = $14,000 × (1 + 2%) ^2 × (1 + 4%) ^3

                                       = $14,000 × 1.0404 × 1.1249

                                       = $14,000 × 1.1703

                                       = $16,384.32

Hence, if inflation rate is 2% for first 2 year and 4% for next three year then price of car is $16,384.32