Question

If an ounce of gold, valued at $734, increases at a rate of 9.3 percent per year, how long (in years) will it take to be valued at $3,000? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

Given,

Present value = $734

Increasing rate = 9.3% or 0.093

Future value = $3000

Solution :-

Let number of years be 'n'

Future value = present value x (1 + increasing rate)ⁿ

$3000 = $734 x (1 + 0.093)ⁿ

$3000/$734 = (1.093)ⁿ

4.08719346049 = (1.093)ⁿ

Taking 'log' both sides,

Log(4.08719346049) = Log(1.093)ⁿ

Log(4.08719346049) = n.Log(1.093)

1.407858539 = n.(0.08892620919)

1.407858539/0.08892620919 = n

15.83 = n

So, it will take 15.83 years to be valued at $3000.