you deposit $400 each month into an account earning 6% interest compounded monthly.\na) how much will you…

Explanation:

Step1: Identify the variables for the future - value of an ordinary annuity formula

The monthly deposit $P = 400$, the annual interest rate $r=6%=0.06$, so the monthly interest rate $i=\frac{0.06}{12}=0.005$, and the number of periods $n = 15\times12 = 180$ months. The formula for the future - value of an ordinary annuity is $F = P\times\frac{(1 + i)^{n}-1}{i}$.

Step2: Calculate the future value of the annuity (answer to part a)

Substitute the values into the formula: [ \begin{align*} F&=400\times\frac{(1 + 0.005)^{180}-1}{0.005}\ &=400\times\frac{(1.005)^{180}-1}{0.005} \end{align*} ] First, calculate $(1.005)^{180}\approx2.4540935$. Then $(1.005)^{180}-1\approx1.4540935$. And $\frac{(1.005)^{180}-1}{0.005}=\frac{1.4540935}{0.005}=290.8187$. So $F = 400\times290.8187=116327.48$.

Step3: Calculate the total amount deposited (answer to part b)

The monthly deposit is $P = 400$, and the number of months $n = 180$. The total amount deposited $A=P\times n=400\times180 = 72000$.

Step4: Calculate the total interest earned (answer to part c)

The total interest $I$ is the future value of the account minus the total amount deposited. So $I=F - A=116327.48-72000 = 44327.48$.

Answer:

a) $116327.48 b) $72000 c) $44327.48