Chapter 6.6, Problem 25IP

To determine

To find: Which option will yield more money.

Answer to Problem 25IP

Option A using simple interest we can yield more money.

Explanation of Solution

Given information:

Principal amount $=\$1500$

Simple interest percent $=6.25\%$ .

Compound Interest percent $=5.75\%$

Time $=3$ years

If compounded annually value of $n$ is $1$ .

Concept:

Simple interest:

  $I=prt$

Where

  $I=$ Simple interest.

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

Compound interest:

  $A=p{\left(1+\frac{r}{n}\right)}^{nt}$

Where

  $A=$ Total amount

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

  $n=1$ for compounded annually.

Calculation:

Using simple interest From given information

Time $=t=3$ years.

Principal amount $=p=\$1500$ .

Interest percent $=R=6.25\%$

We know

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

  $\begin{array}{l}\Rightarrow r=\frac{6.25}{100}\\ \Rightarrow r=0.0625\end{array}$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}I=prt\\ \Rightarrow I=\left(1500\right)\left(0.0625\right)\left(3\right)\\ \Rightarrow I=281.25\end{array}$

Therefore,

Final amount $=$ Principal amount $+$ Simple interest.

  $\Rightarrow$ Final amount $=$$1500+281.25=\$1781.25$

Therefore,

Final amount using simple interest is $\$1781.25$

Using Compound interest From given information

Time $=t=3$ years.

Principal amount $=p=\$1500$ .

Interest percent $=r=5.75\%=0.0575$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}A=p{\left(1+\frac{r}{n}\right)}^{nt}\\ \Rightarrow A=1500{\left(1+\frac{0.0575}{1}\right)}^{3\left(1\right)}\\ \Rightarrow A=1500{\left(1+0.0575\right)}^3\\ \Rightarrow A=1500{\left(1.0575\right)}^2\\ \Rightarrow A=1500\left(1.18260886\right)\\ \Rightarrow A=\$1773.91\end{array}$

Therefore,

To nearest cent, Total amount using compound interest $=A=\$1773.91$

We got

Final amount using simple interest is $\$1781.25$

Total amount using compound interest $=A=\$1773.91$

Therefore,

On comparing both values

We can say that

Option A using simple interest we can yield more money.