A Brand New Car Worth Php 800,000,Depreciates With The Following Sequence It Is Worth Php 772,000 After One Year,Php 744,980 After Two Years.How Much

A brand new car worth Php 800,000,depreciates with the following sequence it is worth Php 772,000 after one year,Php 744,980 after two years.How much does it worth after 5 years?

 

Answer:

The car is worth Php 693,744.00 after 5-year depreciation.

Step-by-step explanation:

a₁ (first year) = 800,000

a₂ (second year) = 772,000

a₃ (third year) = 744,980

To find how many percent the car value depreciates each year:

a₂/a₁ = a₃/a₂

772,000/800,000 = 744,980/772,000

0.965 = 0.965

Common Ratio = 0.965

n = 5 (number of years)

a₁ = 800,000

a₅ = Unknown (the car value after 5 years)

Geometric sequence:

an = a₁ (r)ⁿ⁻¹

a₅ = 800,000 (0.965)⁵⁻¹

a₅ = 800,000 (0.965)⁴

a₅ = 800,000 (0.867180000625)   (Use calculator)

a₅ = 693,744.00