Chapter 5.7, Problem 49AYU

Comparing Savings Plans Jim places $\$1000$ in a bank account that pays $5.6\%$ compounded continuously. After 1 year, will he have enough money to buy a computer system that costs $\$1060$? If another bank will pay Jim $5.9\%$ compounded monthly, is this a better deal?

To determine

To find: Comparing Savings Plans Jim places $\text{\$1000}$ in a bank account that pays $\text{5}\text{.6\%}$ compounded continuously. After 1 year, will he have enough money to buy a computer system that costs $\text{\$1060}$? If another bank will pay Jim $\text{5}\text{.9\%}$ compounded monthly, is this a better deal?

Answer to Problem 49AYU

Solution:

The amount not enough to buy a computer, since Jim will have $\$1057.60$ after 1 year. The second bank gives a better deal; Since Jim will have $\$1060.62$ after 1 year

Explanation of Solution

Given

$P=1000, r=5.6\%=0.056$ and $t=1$

Calculation:

$A=P{e}^{rt}$

$A=1000e^{0.056\left(1\right)}$

$=1000e^{0.056}$

$=1057.60$

The amount not enough to buy a computer, since Jim will have $\$1057.60$ after 1 year

Given $P=1000, r=5.9\%=0.059, n=12$ and $t=1$

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

$A=1000{\left(1+\frac{0.059}{12}\right)}^{12\left(1\right)}$

$=1000{\left(1+\frac{0.059}{12}\right)}^{12}$

$=1060.62$

The second bank gives a better deal; Since Jim will have $\$1060.62$ after 1 year.