after college gerald wants to take a graduation trip to china. he wants to save $4,000 for his trip in four…

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 (monthly savings), $r$ 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 the interest is compounded monthly, $n = 4\times12=48$ months, and $F = 4000$. We need to solve the formula for $A$: [A=\frac{F\times r}{(1 + r)^{n}-1}]

Step2: Substitute the values into the formula

[r=\frac{0.07}{12}\approx0.005833] [(1 + r)^{n}=(1 + 0.005833)^{48}] Using the formula for compound - interest $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply using a calculator, $(1+0.005833)^{48}\approx1.322577$. [A=\frac{4000\times\frac{0.07}{12}}{(1+\frac{0.07}{12})^{48}-1}=\frac{4000\times0.005833}{1.322577 - 1}=\frac{23.332}{0.322577}\approx72.33\approx72]

Answer:

B. $72