Chapter 12.6, Problem 20STP

To determine

To calculate: the amount Mr.Bahn invested at 7%.

Answer to Problem 20STP

Mr.Bahn invested $8000 at 7%

Explanation of Solution

Given information:

Mr.Bahn has $20,000 to invest

He invests part at 6%and rest at 7%

He earns $1280 in interest within a year.

Formula used:

Simple interest $=\frac{p\times t\times r}{100}$p represents amount invested

rrepresents rate of interest

t represents time (year)

Calculation:

Let the amount invested at 7 % be x

Therefore amount invested at 6% is $\left(20000-x\right)$

Yearly earn at 7 % $=\frac{x\times 1\times 7}{100}$

Yearly earn at 6 % $=\frac{\left(20000-x\right)\times 1\times 6}{100}$

Equate total yearly earn

  $\begin{array}{l}\frac{\left(20000-x\right)\times 1\times 6}{100}+\frac{x\times 1\times 7}{100}=1280\\ \left(120000-6x\right)+7x=128000\left[\text{multiply both sides by 100}\right]\\ 120000-6x+7x=128000\\ x=128000-120000\left[\text{subtract 120000 from both sides }\right]\\ x=8000\end{array}$

Therefore,

Mr.Bahn invested $8000at 7%