Chapter 9, Problem 6STP

To determine

Amount borrowed at 4% rate of interest.

Answer to Problem 6STP

• Amount borrowed at 4% = $1250

Explanation of Solution

Given Data:

• Annual interest = $500
• One part borrowed at 6% & other at 4%
• Amount borrowed at 6% is six times the amount borrowed at 4%

Calculation:

  $\begin{array}{l}\text{Let the amount borrowed at 4\% = \$ x}\\ \text{Then,}\\ \text{Amount borrowed at 6\% = \$ 6x}\\ \text{Now,}\\ \text{S}\text{.I}\text{. = }\frac{\text{P}\times \text{R}\times \text{T}}{100}\\ \text{S}\text{.I}{\text{.}}_{(\text{at 4\%)}}=\frac{\mathrm{x}\times 4\times 1}{100}\mathrm{.................................}(1)\\ \text{S}\text{.I}{\text{.}}_{\text{(at 6\%)}}=\frac{6\mathrm{x}\times 6\times 1}{100}\mathrm{................................}(2)\\ \text{Total Interest = \$500}\\ \text{Thus,}\\ \text{Total Interest = (1)+(2)}\\ \Rightarrow \text{500 = }\frac{\mathrm{x}\times 4\times 1}{100}+\frac{6\mathrm{x}\times 6\times 1}{100}\\ \Rightarrow 500=\frac{4\mathrm{x}}{100}+\frac{36\mathrm{x}}{100}\\ \Rightarrow 500=\frac{40\mathrm{x}}{100}\\ \Rightarrow \mathrm{x}=\frac{500\times 100}{40}\\ \Rightarrow \mathrm{x}=1250\\ \text{Therefore,}\\ \text{Amount Borrowed at}\\ \text{4\% = \$1250}\\ \text{6\% = \$7500}\end{array}$

Conclusion:

Amount borrowed at 4% = $1250