Question

+Suppose you want to have $400,000 for retirement in 30 years. Your account earns 10% interest. Round your answers tothe nearest cent.a) How much would you need to deposit in the account each month?b) How much interest will you earn?Question Help: D Post to forum

Answer 1

We are asked to determine the initial value for an account with 10% interest and a time frame of 30 years. To do that we will use the following formula:

`P=(A((r)/(n)))/((1+(r)/(n))^(nt)-1)`

Where:

`\begin{gathered} A=\text{ future value} \\ P=\text{ Present value} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \\ n=\text{ number of compounded periods} \end{gathered}`

Now, we determine the interest rate in decimal form by dividing by 100:

`r=(10)/(100)=0.1`

If the interest is compounded monthly then we have that :

`n=12`

Now, we plug in the values:

`P=((400000)((0.1)/(12)))/((1+(0.1)/(12))^((12)(30))-1)`

Now, we solve the operations:

`P=176.95`

Therefore, the monthly amount is $176.95.

Part B. To determine the interest we need to determine the total amount paid during the 30 years. Since the payments are made each month we need to determine the number of months is 30 years:

`30\text{years}*(12month)/(1year)=360months`

Now, we multiply the monthly payments by the number of months:

`176.95*360=63702`

Now, we subtract this to the $400000 we get:

`I=400000-63702=336298`

Therefore, the interest gained is $336298.