The value of a collector's item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years. $578.81 $607.75 $1687.50 $2531.25

  $607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

  $500 × 1.21550625 = $607.753125 ≈ $607.75

ratio is 2 : 9

the answer is three

13.5 : 3