7.3 learning m.o.m. annuities & other investments (25 pts)\nscore: 12.6/19 answered: 10/11\nquestion…

Explanation:

Step1: Identify the annuity - formula variables

The future - value of an ordinary annuity formula 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 $i = 7%=0.07$, so the monthly interest rate $r=\frac{0.07}{12}$, and the number of months $n = 30\times12=360$ months, and $F = 700000$.

Step2: Solve for the monthly deposit $A$

From $F = A\times\frac{(1 + r)^{n}-1}{r}$, we can re - arrange it to $A=\frac{F\times r}{(1 + r)^{n}-1}$. Substitute $F = 700000$, $r=\frac{0.07}{12}$, and $n = 360$ into the formula: [ \begin{align*} A&=\frac{700000\times\frac{0.07}{12}}{(1+\frac{0.07}{12})^{360}-1}\ \end{align*} ] First, calculate $(1+\frac{0.07}{12})^{360}\approx7.612255$. Then $(1+\frac{0.07}{12})^{360}-1\approx6.612255$. And $700000\times\frac{0.07}{12}\approx4083.33$. So $A=\frac{4083.33}{6.612255}\approx617.54$.

Step3: Calculate the total amount of deposits

The total amount of deposits is the monthly deposit amount times the number of months. The total deposits $=A\times n=617.54\times360 = 222314.4$.

Step4: Calculate the interest earned

The interest earned $I$ is the future value minus the total amount of deposits. So $I=700000 - 222314.4=477685.6$.

Answer:

a) $617.54$ b) $477685.6$