Question

In​ 1990, the average income for an American worker was​ $1,518 per month. In​ 2000, the average income for an American worker was​ $2,632 per month. During this time​ period, a basket of necessities​ (food, housing,​ etc.) increased from​ $657 per month in 1990 to​ $1,402 per month in 2000.

The real value of income
▼
increased
decreased
over that​ 10-year period.

Answer 1

Decreased

Explanation:

-The rate of growth in food prices can be calculated using the compound interest formula as:

`A=P(1+i)^t\\\\1402=657(1+i)^(10)\\\\(1+i)=((1402)/(657))^(0.1)\\\\1+i=1.07874\\\\i=0.07874`

We use the calculated growth rate in food prices to find the potential future value of a 90's income:

`A=P(1+i)^n\\\\=1518(1.07874)^(10)\\\\=3239.21`

#Compare this calculated value to the stated value:

`3239.21>2632`

Hence, the real value of income has decreased since it's less than it's future value over the 10-year period.