The 1 alue of Alex's van could also be depreciated using the reducing balance method of depreciation. The value of the van, in dollars, after $$ n $$ years, $$ R_{n} $$, can be modelled by the recurrence relation show below. $$ R_{0}=75000, R_{n+1}=0.943 R_{n} $$ At what annual percentage rate is the value of the van depreciating each year? Write your answer...

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We are given the recurrence relation:

$$
R_{0} = 75000, \quad R_{n+1} = 0.943 \, R_{n}
$$

This indicates that each year the value of the van is multiplied by $$0.943$$.

The multiplicative factor per year is $$0.943$$, which means:

$$
1 - \text{depreciation rate} = 0.943
$$

Thus, the annual depreciation rate is:

$$
\text{Depreciation rate} = 1 - 0.943 = 0.057
$$

Converting this to a percentage:

$$
0.057 \times 100\% = 5.7\%
$$

Therefore, the value of the van is depreciating at an annual rate of $$5.7\%$$.
The van is depreciating at an annual rate of 5.7%.

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