Determine how long in years it will take the value of a motor vehicle to decrease to 25% of its original value if the rate of depreciation based on the reducing balance method is 21% per annum?
100 (1- .21)^t = 25
.79^t = .25
log (.79^t) = log .25
t log.79 = log.25
t = log.25/log.79 = 13.66
about 13 and 2/3 years
1.6
To determine how long it will take for the value of a motor vehicle to decrease to 25% of its original value using the reducing balance method, we need to find the number of years that corresponds to a depreciation of 75% (100% original value - 25% final value).
The reducing balance method calculates depreciation as a percentage of the remaining value each year, rather than a fixed percentage of the original value. In this case, the rate of depreciation is given as 21% per annum.
To solve this problem, we can use the formula for compound interest:
Final Value = Original Value * (1 - Rate of Depreciation)^n
Where:
- Final Value is the remaining value after n years,
- Original Value is the initial value (100%),
- Rate of Depreciation is the annual depreciation rate (21%),
- n is the number of years.
Substituting the values into the formula, we can solve for n:
0.25 = 1 * (1 - 0.21)^n
Simplifying:
0.25 = (0.79)^n
Taking the logarithm of both sides (base 10 or natural logarithm can be used):
log(0.25) = n * log(0.79)
n = log(0.25) / log(0.79)
Using a calculator, we can evaluate this expression:
n ≈ 5.644
Therefore, it will take approximately 5.644 years for the value of the motor vehicle to decrease to 25% of its original value using the reducing balance method with a depreciation rate of 21% per annum.