Chapter 5.7, Problem 56AYU

Per Capita Federal Debt In $2018$, the federal debt was about $\$21$ trillion. In $2018$, the U.S. population was about $327$ million. Assuming that the federal debt is increasing about $5.5\%$ per year and the U.S. population is increasing about $0.7\%$ per year, determine the per capita debt (total debt divided by population) in $2030.$

To determine

To calculate: The per capita debt in $2030$, if the federal debt of $\$21$ trillion increasing about $5.5\%$ per year and U.S. population of $327$ million, increasing about $0.7\%$ per year from $2018$ to $2030$

Answer to Problem 56AYU

Solution:

The per capita debt of U. S. in 2030 will be $\$112149.88$.

Explanation of Solution

Given information:

The federal debt of $\$21$ trillion increasing about $5.5\%$ per year from $2018$ to $2030$

The U.S. population of $327$ million increasing about $0.7\%$ per year from $2018$ to $2030$

Formula used:

The compound interest formula is $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Calculation:

Use the compound interest formula to find the total debt with $P=21$, $r=0.055$, $n=1$ and $t=12$ to find $A$.

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

$A=21{\left(1+\frac{0.055}{1}\right)}^{(1\cdot 12)}$

$A=39.9253572$ trillion

Where $1$ trillion $=10,00,000$ million

Hence, $39.9253572$ trillion $=39925357.2$ million

The total debt in 2030 will be $\$39925357.2$ million

Let’s use the compound interest formula, to find the total population of U.S with $P=327$, $r=0.007$, $n=1$ and $t=12$ to find $A_P$.

$A_P=327{\left(1+\frac{0.007}{1}\right)}^{\left(1\cdot 12\right)}$

$A_P=355.55$

Hence, the total population of U.S in $2030$ will be $356$ million.

So, the per capita debt $=\frac{A}{A_P}=\frac{39925357.2}{356}\approx 112149.88$

Hence, the per capita debt in 2030 will be $\$112149.88$.