Chapter ISG, Problem 7.1.6P

a.

To determine

To write equations

Answer to Problem 7.1.6P

  $A=P{(7.2)}^{nt}$ and $A=P{(7.12)}^{nt}$ are the equations

Explanation of Solution

Given:

Option 1: rate of interest: 6.2% per annum compounded

Option 2: rate of interest 0.51% per month compounded

Calculation:

A= $P{(1+r)}^{nt}$

Where, $P$ is principle amount, $r$ rate of interest, t in number of years and n number of times interest compounded

For option 1:

Substituting values,

A = $P{(1+6.2)}^{nt}$

Solving,

  $A=P{(7.2)}^{nt}$   (1)

Option 2:

As known, 1 year=12 months

Rate of interest for 1 month=0.51%

Rate of interest for 12 month=0.51 $\times$ 12%

Solving,

Rate of interest for 12 month=6.12%

Now, substituting value in formula,

A = $P{(1+6.12)}^{nt}$

Solving,

  $A=P{(7.12)}^{nt}$   (2)

Hence, (1) and (2) are the equation.

b.

To determine

To find the better investment.

Answer to Problem 7.1.6P

Option 1 is better.

Explanation of Solution

Given:

Interest rates of investments

Option 1 is the better option because the rate of interest is better in the option 1. It yields better returns