suppose you have $14,000 to invest. which of the two rates would yield the larger amount in 4 years: 7%…

Explanation:

Step1: Calculate amount for 7% compounded monthly

Use compound - interest formula $A = P(1+\frac{r}{n})^{nt}$, where $P=$14000$, $r = 0.07$, $n = 12$ (monthly compounding), and $t = 4$. $A_1=14000(1 +\frac{0.07}{12})^{12\times4}$ $A_1=14000(1+\frac{0.07}{12})^{48}$ $\frac{0.07}{12}\approx0.005833$, $1+\frac{0.07}{12}\approx1.005833$ $(1.005833)^{48}\approx1.32107$ $A_1 = 14000\times1.32107=$18494.98$

Step2: Calculate amount for 6.85% compounded continuously

Use continuous - compounding formula $A = Pe^{rt}$, where $P = 14000$, $r=0.0685$, and $t = 4$. $A_2=14000e^{0.0685\times4}$ $A_2=14000e^{0.274}$ $e^{0.274}\approx1.3159$ $A_2=14000\times1.3159=$18422.6$

Step3: Compare the two amounts

Since $A_1 = 18494.98$ and $A_2 = 18422.6$, and $18494.98>18422.6$.

Answer:

7% compounded monthly