Question

Today, your dream car costs $61,100. You feel that the price of the car will increase at an annual rate 2.1 percent. If you plan to wait 5 years to buy the car, how much will it cost at that time?

Answer 1

Answer: $67,515.50

Step-by-step explanation:

Given Data:

Cost of car = $61,100

Annual increase in rate = 2.1%

Waiting duration = 5 years

Therefore:

Increase in Cost of car when waiting for 1 year

= interest of 1year + Original cost

= $61,100 * 0.021 + $61,100

= $1283.1 + $61,100

= $62,383.1

Increase in cost of car when waiting for 5 years before purchase

= Increases in rate + Original cost

= 0.021 * 5 * $61,100 + $61,100

= $6,415.5 + $61,100

= $67,515.5

After 5 years the car would cost approximately $67,515.50

Answer 2

$67,679.72

Step-by-step explanation:

current price = $61,100

if the price increases 2.1% per year, to find out the price in 5 years we need to use the future value formula for exponential growth:

future value = present value x (1 + rate)ⁿ

FV = $61,100 x (1 + 0.021)⁵ = $61,100 x 1.1095 = $67,679.72

The exponential growth rate formula measures the growth rate in time with proportionally to the quantity itself. It is the same formula used to calculate compound interest, i.e. earned interest starts to earn more interest by itself. In this case, the difference between the old and new price starts to increase as time passes.