MHB How to Solve Investment Word Problems Involving Interest Rates and Profits?

  • Thread starter Thread starter bergausstein
  • Start date Start date
bergausstein
Messages
191
Reaction score
0
1. A trust fund has invested \$8000 at 6% annual interest.
How much additional money should be invested at
8.5% to obtain a return of 8% on the total amount
invested?

my solution,

let
$n=$amount invested @ 8.5%

$0.06(8000)+0.085n=0.08(8000+n)$

$480+0.085n=640+0.08n$

$0.085n-0.08n=640-480$

$n=32,000$

\$32,000 is the addtional money should be invested at 8.5%. is this correct?

2. A businessman invested a total of \$12,000 in two ven-tures. In one he made a profit of 8% and in the other he
lost 4%. If his net profit for the year was $120, how
much did he invest in each venture?

in this problem i don't know how will i represent the amount invested in the other venture. please help. thanks!
 
Mathematics news on Phys.org
1.) Correct.

2.) Let $x$ represent the first investment amount and $y$ represent the other. So we know:

$$x+y=12000$$

And we also know:

$$0.08x-0.04y=120$$

which I would rewrite as:

$$2x-y=3000$$

Now, add the two equations to eliminate $y$, then solve for $x$, then use this value of $x$ in either of the two equations to determine $y$.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top