Chapter 6, Problem 18CR

a.

To determine

To write: a function that represents the balance after t years.

Answer to Problem 18CR

  $y=750{\left(1.0125\right)}^{4t}$

Explanation of Solution

Given:

Principal amount = $750

Interest rate = 5% per annum

Compounded quaterly

Concept used:

Compound Interest:

  $y=P{\left(1+\frac{r}{n}\right)}^{nt}$ ….. (1)

Where P is principal, r is annual interest rate (in decimal form), t is time in years and n is the number of times interest is compounded per year.

Calculation:

Substituting $P=750$ , $n=4$ and $r=0.05$ in equation (1),

  $\begin{array}{c}y=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =750{\left(1+\frac{0.05}{4}\right)}^{4t}\\ =750{\left(1.0125\right)}^{4t}\end{array}$

Conclusion:

So, the balance in the account after t years is given by the function $y=750{\left(1.0125\right)}^{4t}$.

b.

To determine

the balance in the account after 4 years.

Answer to Problem 18CR

Approximately $\$915$

Explanation of Solution

Given:

The balance in the account after t years is given by the function:

  $y=750{\left(1.0125\right)}^{4t}$

The balance in the account after 4 years is found by substituting $t=4$ in the above function.

  $\begin{array}{c}y\left(4\right)=750{\left(1.0125\right)}^{4\times 4}\\ \approx 914.92\end{array}$

Conclusion:

So, balance in the account after 4 years will be about $915.