suppose that a family wants to start a college fund for their child. if they can get a rate of 5.2%…

Explanation:

Step1: Identify the formula for the future - value of 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, $r$ is the interest rate per period, and $n$ is the number of periods. The annual interest rate $i = 5.2%=0.052$. Since it is compounded monthly, the interest rate per month $r=\frac{0.052}{12}$. The number of years $t = 20$, so the number of periods $n=20\times12 = 240$ months, and $F = 55500$. We need to solve the formula for $A$: [A=\frac{F\times r}{(1 + r)^{n}-1}]

Step2: Substitute the values into the formula

First, calculate $r=\frac{0.052}{12}\approx0.004333$. Then, calculate $(1 + r)^{n}=(1 + 0.004333)^{240}$. Using the formula $a^{b}=e^{b\ln(a)}$, we have $(1 + 0.004333)^{240}=e^{240\times\ln(1.004333)}$. $240\times\ln(1.004333)=240\times0.004324 = 1.03776$. $e^{1.03776}\approx2.8221$. $(1 + r)^{n}-1=2.8221 - 1=1.8221$. $F\times r=55500\times0.004333 = 240.3815$. [A=\frac{240.3815}{1.8221}\approx131.93]

Answer:

a. $131.93$