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
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