Video Transcript
The value of an antique painting increases every year. The painting is currently worth 12,000 dollars and is expected to be worth 20,000 dollars in eight years’ time. Write an equation that can be used to find 𝑟, the rate at which its value increases.
So, in this question, we’re told that there is a painting which is currently worth 12,000 dollars. However, in eight years, it will be worth 20,000 dollars. We therefore need to work out the rate at which this painting’s value increases. Although it might not immediately be obvious, we can find the answer to this question by applying the compound interest formula. This formula gives us that 𝑣, the value of the return, is equal to 𝑝 times one plus 𝑟 over 100 to the power of 𝑦, where 𝑝 is the principal or starting amount, 𝑟 is the rate, and 𝑦 is the number of years.
So, let’s jot down any information that we’re given in the question. Often, we need to calculate the value of the return. But in this case, we know it; it’s the value that the painting will be in eight years’ time. That’s 20,000 dollars. The starting amount is what the painting is currently worth, which is 12,000 dollars. We don’t know the interest rate, but we want to keep the equation in terms of 𝑟. And finally, the number of years is eight years.
We can now fill these values into the formula. This gives us 20,000 equals 12,000 times one plus 𝑟 over 100 to the power of eight. We can keep our answer like this or as 12,000 times one plus 𝑟 over 100 to the power of eight equals 20,000. Either forms would allow us to calculate the rate at which the value of this painting increases.
