You buy a new computer for $2100. The computer is decreases by 5% annually. When will the computer have a value of $600?
Y = a(1+r/n)^n(t)
Y = 5.25
You want t years, where
2100(0.95)^t = 600
0.95^t = 2/7
t = log(2/7)/log(0.95) = 24.42
To find when the computer will have a value of $600, we can use the formula for compound interest, where:
Y is the final value of the computer
a is the initial value of the computer
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the initial value (a) is $2100, and the computer decreases by 5% annually, which means the annual interest rate (r) is -0.05 (negative because it's a decrease).
Let's rearrange the formula to solve for t:
t = log(Y/a) / (n log(1+r/n))
Now let's substitute the given values:
Y = $600
a = $2100
r = -0.05 (annual decrease of 5%)
n = 1 (since the interest is compounded once a year)
Plugging in these values:
t = log($600 / $2100) / (1 log(1 - 0.05/1))
Using a calculator, we can calculate the value of t:
t = log(0.2857) / (1 log(0.95))
t = -1.2497 / -0.0212
t ≈ 59.033
Therefore, the computer will have a value of $600 after approximately 59 years.