#### The value of a machine worth ₹ 500000 is depreciating at the rate of 10% every year. In how many years will its value be reduced to ₹ 364500?

**Solution:**

It is given that

Present value = ₹ 500000

Reduced value = ₹ 364500

Rate of depreciation = 10% p.a.

Consider n years as the period

We know that

A/P = (1 – r/100)^{n}

Substituting the values

364500/500000 = (1 – 10/100)^{n}

By further calculation

(9/10)^{n} = 729/1000 = (9/10)^{3}

So we get

n = 3

Therefore, the period in which its value be reduced to ₹ 364500 is 3 years.

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