MAT $200$ Inquiry & Problem Solving Project Stocks versus Bonds: Part II

The figure in the New York Times article "Trading Stocks for Bonds Poses Its Own Risks" is shown below.

Return of a $$25,000$ investment over $40$ years, assuming a $3$ percent Inflation rate $$400,000$

Compound Interest Formula

The amount A after $t$ years due to a principal $P$ invested at an annual interest rate $r$ compounded $n$ times per year is

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

According to the New York Times article, "a typical portfolio of stocks might earn $7$ percent on average, compared with the $1\mathrm{.}55$ percent yield of a long$-$term bond these days." Using the compound interest formula, with a principal of $25,000$ and annual compounding, the amount for stocks and bonds, denoted by $A_s$ and $A_b,$ respectively, are