Question

A washing machine was bought at ₹ 15,625 three years ago. If its value depreciates at 16% p.a., calculate

1. its present value
2. its value after one year from now

Answer 1

Given:

• Cost price (initial value) P = ₹ 15,625
• Rate of depreciation r = 16% per year
• Time n = 3 years

Depreciation formula:

`V = P(1 - r/100)^n`

Where V = value after n years.

i. Present value (after 3 years)

`V_("present") = 15,625(1 - 16/100)^3`

`V_("present") = 15,625 xx (0.84)^3`

Step by step:

0.84 × 0.84 = 0.7056

0.7056 × 0.84 = 0.592704

`V_("present")` = 15,625 × 0.592704 ≈ 9,261

Present value: ₹ 9,261

ii. Value after one more year (4th year)

We take the present value as the new principal and apply one more year of 16% depreciation:

`V_("after 1 year") = 9,261 xx (1 - 0.16)`

`V_("after 1 year") = 9,261 xx 0.84`

`V_("after 1 year") ≈ 7,779.24`

Value after one year from now: ₹ 7,779.24