How to find rate of depreciation in this problem?

Question

The value of a machine is estimated to be 27,000 at the end of 1994 and 21,870 at the beginning of 1997. Supposing it depreciates at a constant rate per year of it's value at the beginning of the year, calculate: 1) Rate of depreciation 2) The value of the machine at the end of 1997 and at the beginning of 1994

How do I proceed? Is the time 2 or 3 years?

Where P = principal, CI = compound interest, n = number of years, R = rate

Answer 1

The end of the year is basically the same as the beginning of the next year.

So, if $V_n$ is the value at the beginning of year $n$, then you have the formula $V_{n+1} = (1-r) V_n$ (this formula works 'backwards' as well, that is, you can compute $V_n$ knowing $r$ and $V_{n+1}$), where $r$ is the depreciation rate. You are given $V_{1995}$ and $V_{1997}$, from which you can compute $r$. Then, knowing $r$ you need to calculate $V_{1998}$ and $V_{1994}$.

Answer 2

Hint:

1. $\text{current price} = \text{original price} \times (1 - R)^n.$

2. Visualize the number of years: $\mid - 94 - \mid - 95 - \mid - 96 - \mid - 97 - \mid.$ How many years between the end of '94 and the beginning of '97?