Asked by Jonathan Smith on May 30, 2024
Verified
Murphy's annual income has increased by 10% per year for the last 8 years. If Murphy's annual income is now $72,596, what was it 8 years ago?
A) $14,519
B) $33,867
C) $41,587
D) $51,922
E) $58,077
Per Year
A term indicating something occurs, is measured, or is evaluated on an annual basis.
8 Years
A period or duration of eight calendar years.
Annual Income
The total earnings from work, investment, benefits, and other sources over the course of a year.
- Analyze the growth of investments using different rates and compounding periods.
Verified Answer
DH
Debbi HinderliterJun 01, 2024
Final Answer :
B
Explanation :
To find Murphy's income 8 years ago, we can use the formula for exponential decay, which in this context is the reverse of growth: P=A(1+r)nP = \frac{A}{(1 + r)^n}P=(1+r)nA , where PPP is the principal amount (initial income), AAA is the amount after nnn years (final income), rrr is the rate of increase, and nnn is the number of years. Plugging in the values: P=72,596(1+0.10)8P = \frac{72,596}{(1 + 0.10)^8}P=(1+0.10)872,596 , which simplifies to approximately $33,867.
Learning Objectives
- Analyze the growth of investments using different rates and compounding periods.
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