select the correct answer. after college gerald wants to take a graduation trip to china. he wants to save…

Explanation:

Step1: Identify the compound - interest formula for an ordinary annuity

The formula for the future value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $F$ is the future value of the annuity, $A$ is the amount of each payment (the monthly savings we want to find), $r$ is the interest rate per period, and $n$ is the number of periods. The annual interest rate is $7%=0.07$, so the monthly interest rate $r=\frac{0.07}{12}$. The time period is 4 years, and since there are 12 months in a year, $n = 4\times12=48$ months, and $F = 4000$.

Step2: Rearrange the formula to solve for $A$

Starting with $F = A\times\frac{(1 + r)^{n}-1}{r}$, we can solve for $A$: [A=\frac{F\times r}{(1 + r)^{n}-1}] Substitute $r=\frac{0.07}{12}$ and $n = 48$ and $F = 4000$ into the formula: First, calculate $(1 + r)^{n}=(1+\frac{0.07}{12})^{48}$. Let $x=\frac{0.07}{12}\approx0.005833$. Then $(1 + x)^{48}\approx1.322077$. [(1+\frac{0.07}{12})^{48}-1\approx1.322077 - 1=0.322077] [A=\frac{4000\times\frac{0.07}{12}}{(1+\frac{0.07}{12})^{48}-1}] [A=\frac{4000\times0.005833}{0.322077}=\frac{23.332}{0.322077}\approx72.44\approx72]

Answer:

B. $72