Question 1195246: The value of a house appreciated at the rate of 3.5% per annum. If its original value was sh.2,000,000 calculate the time it would take to appreciate to sh. 2,029,500
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period.
1 + r is the growth factor.
n is the number o time periods.
in this problem, the equation becomes:
2,029,500 = 2,000,000 * 1.035 ^ n
divide both sides of the equation by 2,000,000 to get:
(2,029,500 / 2,000,000) = 1.035 ^ n
take the log of both sides of the equation to get:
log(2,029,500 / 2,000,000) = log(1.035 ^ n)
by log laws, this becomes:
log(2,029,500 / 2,000,000) = n * log(1.035)
solve for n to get:
log(2,029,500 / 2,000,000) / log(1.035) = n = .4256299268.
confirm by replacing n in the original equation to get:
f = 2,000,000 * 1.035 ^ .4256299268 = 2,029,500.
this confirms the value of n is correct.
your solution is that it would take .4256299268 years for 2,000,000 to becomes 2,029,500.
that's a little less than half a year.
for your information, the log law used was.
log(x ^ a) = a * log(x)
here's a reference.
https://www.andrews.edu/~calkins/math/webtexts/numb17.htm
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