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Question 1156235: the annual rate of inflation, in percent, of a home that increases in value from p to q over a period of n years is i=100((q)/(p))^((1)/(n))-100 find the annual rate of inflation, to the nearest tenth of a percent, of a home that doubles in value over 20 years
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! my formula is:
f = p * (1 + r) ^ 20
f = future value
p = present value
r = interest rate per time period (years in this case)
n = number of time periods (years in this case.
in your problem, the formula becomes:
2 = 1 * (1 + r) ^ 20
this simplifies to:
2 = (1 + r) ^ 20
take the 20th root of both sides of this equation to get:
2 ^ (1/20) = 1 + r
solve for 1 + r to get:
1 + r = 1.035264924
that's your annual growth factor.
your annual rate of inflation is that minus 1 = .035264924.
confirm by replacing r in the equation to get:
2 = (1 + .035264924) ^ 20
simplify to get:
2 = 2
this confirms the rate is correct.
multiply it by 100 to get the percent.
that makes your annual rate of inflation equal to 3.5264924%.
your formula is:
i=100((q)/(p))^((1)/(n))-100
when q doubles from p over 20 years, your formula becomes:
i = 100 * (2 / 1) ^ (1 / 20) - 100.
solve for i to get:
i = 3.526492384%
your formula gets you the same answer as my formula.
that means the formulas are equivalent, even though they look different.
you should be able to device your formula from my formula.
start with f = p * (1 + r) ^ n
replace f with q and leave p as is to get:
q = p * (1 + r) ^ n
divide both sides of the equation by p to get:
q / p = (1 + r) ^ n
take the nth root of both sides of the equation to get:
(q / p) ^ (1/n) = 1 + r
subtract 1 from both sides of the equaion to get:
(q / p) ^ (1/n) -1 = r
multiply both sides of the equation by 100 to get:
100 * (q/p) ^ (1/n) - 100 = r%
let r% = i and you get:
100 * (q/p) ^ (1/n) - 100 = i
switch sides in the equation to get:
i = 100 * (q/p) ^ (1/n) - 100
put some additional parentheses in there that weren't really necessary and and get rid of some of the operators that are assumed to be there and get rid of the spaces that don't really need to be there and you get:
i=100((q)/(p))^((1)/(n))-100.
here's your formula and my converted formula right below it for you to see that they're identical.
i=100((q)/(p))^((1)/(n))-100 (your formula)
i=100((q)/(p))^((1)/(n))-100 (my converted formula).
they're identical.
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