Question

A company has invested K32000 in artwork that it predicts will increase in value by 12% per year. Find the number of years before the value of the artwork has doubled in value. Use the formula A equals P times R to the power of n, where A is the amount accumulated, P is the principle, R is the rate, and n is the term or time.

Answer 1

Given:
P = K32000
R = 0.12
We want to find n when A = 2P

Substitute these values into the formula:

2P = P * (1 + 0.12)^n

Simplify:

2 = (1.12)^n

Take the natural logarithm of both sides to solve for n:

ln(2) = n * ln(1.12)

n = ln(2) / ln(1.12)
n ≈ 6.1186

Therefore, it will take approximately 6 years before the value of the artwork has doubled.

Answer 2

The correct answer is 7 years

Answer 3

I apologize for the oversight in the calculation. Let's correct it.

n = ln(2) / ln(1.12)
n ≈ 6.1186

Rounded up to the nearest whole number, it will take 7 years before the value of the artwork has doubled. Thank you for pointing out the error.