Chapter 7, Problem 52RE

To determine

To calculate: The amount placed in each investment.

Answer to Problem 52RE

Amount invested in first investment is $x=\$17,000$ , amount invested in second investment is $x-2000=15,000$ and amount invested in third investment is $x-3000=\$14,000$

Explanation of Solution

Given information:An amount of $\$46,000$ is divided among three investments yielding $\$3020$ in interest per year. The interest rates for the three investments are $5\%$ , $7\%$ and $8\%$ simple interest. Second and third amounts are $\$2000$ and $\$3000$ less than the first, respectively.

Calculation:

Let’s assume amount invested in first investment is $x$ , $\therefore$ amount invested in second investment is $x-2000$ and amount invested in third investment is $x-3000$

Now, the simple interest can be calculated by the formula, $I=\frac{PRN}{100}$

  $\therefore$ Interest on first amount, $I_1=\frac{5x}{100}$ , Interest on second amount, $I_2=\frac{7(x-2000)}{100}$ and Interest on third amount, $I_3=\frac{8(x-3000)}{100}$

Now, total amount is $\$46,000$ and total interest is $\$3020$

  $\begin{array}{l}x+x-2000+x-3000=46000\\ \therefore x=17,000\end{array}$

  $\begin{array}{l}\frac{5x}{100}+\frac{7x-14000}{100}+\frac{8x-24000}{100}=3020\\ \therefore x=17,000\end{array}$

  $\therefore$ Amount invested in first investment is $x=\$17,000$ , amount invested in second investment is $x-2000=15,000$ and amount invested in third investment is $x-3000=\$14,000$