Chapter 7.7, Problem 41STP

To determine

Which of the following plan will earn more interest :

1. Principle : $ 500, time : 5 years, simple interest rate : 6.75%
2. Principle : $500, time : 5 years, compound interest rate : 6.5 %

Answer to Problem 41STP

Plan B will earn greater earning.

Explanation of Solution

Given information: Following two investment plans are given:

Plan A : Principle: $ 500, time: 5 years, simple interest rate: 6.75%

Plan B : Principle: $500, time: 5 years, compound interest rate: 6.5 %

Formula used: Simple interest $=\frac{\text{Principle amount}\times \text{rate}\times \text{time}}{100}$

And compound interest $=\text{Principle}{(1+\frac{\text{rate}}{100})}^{\text{time}}-\text{Principle}$

Calculation: Simple interest earned on plan A $=\frac{500\times 6.75\times 5}{100}=25\times 6.75=\text{\$}168.75$

And compound interest earned on plan B $=500{(1+\frac{6.5}{100})}^5-500$

  $\begin{array}{l}$ =500{(1.065)}^5-500$=500\times 1.37-500=685.04-500\\ =\text{\$}185.04\end{array}$

Conclusion: By above calculation, it is cleared that plan B earns more interest.