4.)A diamond is purchased for $3500. Its value increases 5% each year. Find the value of the diamond after six years.
To find the value of the diamond after six years, we can use the formula for compound interest:
Value = Principal * (1 + Rate/100)^Time
In this case, the principal is $3500, the rate of increase is 5% (0.05 in decimal form), and the time is six years.
Plugging in the values into the formula, we get:
Value = $3500 * (1 + 0.05)^6
Calculating the expression inside the parentheses first, we have:
(1 + 0.05)^6 = 1.05^6 ≈ 1.3401
Now we can substitute this value back into the formula:
Value = $3500 * 1.3401
Evaluating the multiplication, we find that the value of the diamond after six years is approximately $4690.35.
Therefore, the value of the diamond after six years would be approximately $4,690.35.