Chapter 6.6, Problem 34HP

To determine

To find: Who will have more money over the long run.

Answer to Problem 34HP

Kai-Yo will have more money over the long run.

Explanation of Solution

Given information:

Kai-Yo deposits $\$500$ into an account

Principal amount of Kai-Yo $=\$500$

Simple Interest percent of Kai-Yo $=2\%$

Marcos deposits $\$250$ into an account

Principal amount of Marcos $=\$250$

Simple Interest percent of Marcos $=4\%$

Time for both Marcos and Kai-Yo $=10$ years.

Concept:

  $I=prt$

Where

  $I=$ Simple interest.

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

Calculation:

For Kai-Yo From given information

Principal amount $=p=\$500$

Time $=t=10$ years.

Interest percent $=R=2\%$

We know

Annual interest rate $=r=\frac{R}{100}$

  $\begin{array}{l}\Rightarrow r=\frac{2}{100}\\ \Rightarrow r=0.02\end{array}$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(500\right)\left(0.02\right)\left(10\right)\\ \Rightarrow I=\$100\end{array}$

Therefore,

Total amount of Money Kai-Yo has after 10 years $=$ Principal amount $+$ Simple interest

Total amount of Money Kai-Yo has after 10 years $=$$500+100=\$600$

For Marcos From given information

Principal amount $=p=\$250$

Time $=t=10$ years.

Interest percent $=R=4\%$

We know

Annual interest rate $=r=\frac{R}{100}$

  $\begin{array}{l}\Rightarrow r=\frac{4}{100}\\ \Rightarrow r=0.04\end{array}$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(250\right)\left(0.04\right)\left(10\right)\\ \Rightarrow I=\$100\end{array}$

Therefore,

Total amount of Money Marcos has after 10 years $=$ Principal amount $+$ Simple interest

Total amount of Money Marcos has after 10 years $=$$250+100=\$350$

We got

Total amount of Money Kai-Yo has after 10 years $=$$\$600$

Total amount of Money Marcos has after 10 years $=$$\$350$

Therefore,

Kai-Yo will have more money over a long run.