Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

# Using the depreciation formula V=P(1-r)^n. How do you find r?

Say if P=29990 and V=6000 and n=11

Relevance

V = P(1-r)^n,

P(1-r)^n = V, ===> (1-r)^n = V/P,

OR,

1 -r = (V/P)^1/n,

OR,

r = 1 - (V/P)^1/n >============================< ANSWER

AND

For, P=29990 and V=6000 and n=11,

r = 1 - (6000/29990)^1/11 = 1 - (0.2000667)^1/11,

OR,

r = 1 - 0.18188 = 0.98181 >===========================< ANSWER

• First replace formula with given numbers

6000 = 29990(1-r)^11

6000/29990 = (1- r)^11

using calculator take 11th root of both sides

0.8639 = 1 - r

r = 1 - 0.8639

r = 0.1361

this is in decimal form so multiply by 100 to find percentage rate of depreciation

r = 13.6%

• V=P(1-r)^n

substitute the known values:

6000 = 29990(1-r)^11

divide by 29990

6000/29990 = (1-r)^11

raise to 1/11 power

(6000/29990)^(1/11) = 1-r

(6000/29990)^(1/11) - 1 = -r

r = -(6000/29990)^(1/11) + 1

= 0.1361

• Replace the values given;

6000 = 29990 ( 1 - r ) ^ 11 .......................... Divide by 29990

6000 / 29990 = ( 1 - r ) ^ 11 ........................ Take the 11th root

11 ROOT OF ( 6000/ 29990 ) = 1 - r ............ Solve for r

................ r = 1 - 11th Root ( 6000/ 29990 )

Now you need a scientific calculator to do the division , then take the 11th root. ( You can also raise it to the 1/ 11 power )