# After 4 years of reducing balance depreciation, an asset has a 1/4 of its original value. The original value was R86 000. Calculate the depreciation interest rate, as a percentage. (Correct your...

After 4 years of reducing balance depreciation, an asset has a 1/4 of its original value. The original value was R86 000. Calculate the depreciation interest rate, as a percentage.

(Correct your answer to 1 decimal place.)

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### 1 Answer

The reducing balance formula is `A = P(1-i)^n` where

A = future value, P = present value, i= interest rate, n=years.

Because we are using depreciation, we have used the (1-i) not (1+i) which relates to loans, investments and savings. The reducing balance formula is the same aa the compound interest formula. We calculate P by finding `1/4 times 86 000= 21 500`

`therefore A=P(1-i)^n` becomes `21 500 = 86 000(1-i)^4` . Now manipulate the formula so it can be solved for i.

`21500/86000=(1-i)^4`

`therefore 1/4= (1-i)^4` The opposite operation for power 4 is root 4:

`therefore root(4)(1/4)= (root(4)(1-i))^4`

`therefore 0.7071067812= 1-i` ``

`therefore i=1-0.7071067812`

`therefore i=0.2928...`

To convert into a percentage multiply by 100:

`therefore 0.2928times 100 = 29,28%`

**Ans: (rouned off to one decimal place) = 29,3%**

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