An investment decreases by 10 per year for 4 years By what t

An investment decreases by 10% per year for 4 years. By what total percent does it decrease? The investment decreases by 90.00 % total the tolerance is +/-2%

Solution

we have A = P(1 + r)ⁿ

A = Future value , P = principal , r = -0.1 (negative sign since it is decreasing) , n = 4

==> A = P(1 - 0.1)⁴

==> A = P(0.9)⁴

==> A = P(0.6561)

Initial principal amount has decreased by a factor of 0.6561 after 4 years

==> Total decrease = 1 - 0.6561 = 0.3439

Hence Investement decreases by 34.39% total