Chapter 6.4, Problem 70E

To determine

The two account options that you can deposit $1000 and earn compound interest.

Answer to Problem 70E

The account with higher growth factor, 1.045, should be used since it will yield higher interest.

Explanation of Solution

Given information:

Deposit $1000

The balance of each account after t years

Formula used:

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

Calculation:

The compound interest formula is:

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

Account 1:

The values are determined as P=1000 with r=3% =0.03, n=1

  $\begin{array}{l}y=P{\left(1+\frac{r}{n}\right)}^{nt}\\ y=1000{\left(1+\frac{0.03}{1}\right)}^{1t}\\ y=1000{(}^{1.03}\end{array}$

  $y=1000{\left(1.03\right)}^t$

Account 2:

The values are determined as P=1000 with r=0.045, n=1

  $\begin{array}{l}y=P{\left(1+\frac{r}{n}\right)}^{nt}\\ y=1000{\left(1+\frac{0.045}{1}\right)}^{1t}\\ y=1000{(}^{1.045}\end{array}$

  $y=1000{\left(1.045\right)}^t$

The account with higher growth factor, 1.045, should be used since it will yield higher interest.

Conclusion:

The account with higher growth factor, 1.045, should be used since it will yield higher interest.