A certain population declines by 4% each year. What is the percentage decline each month? (Round your answer to two decimal places.)

An investment declines in value by 5% each month. By what percentage does its value decline in a year? (Round your answer to two decimal places.)

Shaezy Mar 25, 2020

#1**+1 **

1) Since there are 12 months in a year...

-4/12 will be -1/3% or -0.33 decrease each month

CalTheGreat Mar 25, 2020

#2**+1 **

2) There are 12 months in a year....

-5*12=-60.

It declines by 60% or 0.6 each year.

CalTheGreat Mar 25, 2020

#6**+1 **

I'm confused too... I'm so sorry about my incorrect answers. I will look at them again right now!

CalTheGreat Mar 25, 2020

#9**+1 **

Okay. Don't trust me 100%, though. I'm a really rushed, angry elementary school kid... LOL!

CalTheGreat Mar 25, 2020

#22**+1 **

One of the compound interest formula is: F = A(1 + x )^{t}

where F = final amount

A = initial amount

x = interest rate, as a decimal

t = number of years

For this problem, if the inital population = A, then the final population will be 0.96A (because it decreased by 4%).

So: 0.96A = A(1 + x)^{12}

Divide both sides by A: 0.96 = (1 + x)^{12}

Find the 12^{th} root of 0.96: 0.9966039468 = 1 + x

Subtract 1: x = -0.003396 (the '-' indicates that it is decreasing)

geno3141 Mar 25, 2020

#25**+1 **

An investment declines in value by 5% each month. By what percentage does its value decline in a year? (Round your answer to two decimal places.)

Let A be the value of the investment at the beginning of the year

At the end of the year, the investment will be worth

A(.95)^12 ≈ .54036 A

So......the % decline in one year = 1 -.54036 ≈ 45.964% ≈ 45.96%

CPhill Mar 25, 2020