Posted by charlotte on Friday, August 23, 2013 at 12:27pm.
A $5000 investment earns 7.2% annual interest, and an $8000 investment earns 5.4%, both compounded annually. How long will it take for the smaller investment to catch up to the larger one?

precalc  MathMate, Friday, August 23, 2013 at 12:38pm
Use the compound interest formula:
A=P(1+i)^n
A=accumulated amount after n periods (years)
P=principal
i=interest per compounding period
n=number of compounding periods
If the smaller investment catches up to the larger one, then the accumulated amounts would be equal. Therefore by equating the two, we get an equation in which the only unknown is n, the number of periods (years in this case).
5000(1.072)^n=8000(1.054)^n
Solve for n:
(1.072/1.054)^n = 8000/5000
take logs and apply laws of logarithm,
n*log(1.072/1.054) = log(8000/5000)
n=log(8000/5000)/log(1.072/1.054)
I get approximately n=28.
Substitute in above solution to get the exact value.
Answer This Question
Related Questions
 college algebra  An investment initially worth $5300 earns 7.7% annual interest...
 Algebra  Two investments in high technology companies total $1,100. If one ...
 math  How long will it take for an investment of $13,000 to double if the ...
 Math  A Registered Education Savings Plan (RESP) earns interest at a rate of 5...
 interest  Perry has an opportunity to put $12,000 into an investment with an ...
 Math  1. The population,P, in thousands, of a country is P=10^8(1.5)^t/20 where...
 PreCalc  An initial investment of $9000 grows at an annual interest rate of 5...
 Algebra  An investment account earns 4% per year compounded annually. If the ...
 Algebra  An investment account earns 4% per year compounded annually. If the ...
 algebra  An investment account earns 4% per year compounded annually. If the ...
More Related Questions