compound

**agooolka** · November 26th 2011, 07:58 PM

Hi everyone! Can you help me with couple problems

I have a grandson who is just about to be born. He will be here by January 1.

Question #1, what if you were to put $25.oo into a savings account for him every month, for 15 years with interest compounded monthly. At the end of 15 years, you put the total investment value into a savings with no further deposits but compounded monthly. Assume the best you can get is 5% interest. What would he have when he turns 66?

Question #2; Assume you had saved $35.00 a month since you were 18 years old. when you got to be 70, the age at which you must begin withdrawing all retirement plans, how much money would you end with?

Question #3; Assume you had a very wonderful granddad. When you were born, he wanted you to have an investment plan that would give you $1,000,000.00. So, he set it up and he invested until you turned 18. Then, it was your duty to continue the investment. He wanted you to have $1,000,000.00 when you turned 70. Assume the best average interest rate for the period is 7%. what is the amount of monthly deposit that would be required.

**Soroban** · November 26th 2011, 08:52 PM

Hello, agooolka!

I have a grandson who is just about to be born. He will be here by January 1.

Question #1
What if you were to put $25.00 into a savings account for him every month
for 15 years with interest compounded monthly.
At the end of 15 years, you put the total investment value into a savings account
with no further deposits but compounded monthly.

Assume the best you can get is 5% interest.
What would he have when he turns 66?

The first part is an annuity.

The formula is: . $A \:=\:D\,\frac{(1+i)^n-1}{i}$

. . where: . $\begin{Bmatrix}A &=& \text{final balance} \\ D &-& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: . $\begin{Bmatrix}D &=& 25 \\ i &=& \frac{0.05}{12} \\ n &=& 180 \end{Bmatrix}$

Hence: . $A \;=\;25\,\frac{\left(1 + \frac{0.05}{12}\right)^{180} - 1}{0.05} \;=\; 12,\!682.22359$

When your grandson is 15, you will have $12,682.22.

You place this is an account paying 5% per year compounded monthly.

The compound interest formula is: . $A \:=\:P(1 + i)^n$

. . where: . $\begin{Bmatrix}A &=& \text{final balance} \\ P &=& \text{principal invested} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: . $\begin{Bmatrix}P &=& 12,\!682.22 \\ i &=& \frac{0.05}{12} \\ n &=& 612 \end{Bmatrix}$

Hence: . $A \;=\;12,\!682.22\left(1 + \tfrac{0.05}{12}\right)^{612} \;=\;161,\!564.3028$

At age 66, your grandson will have $161,564.30.

**uasac** · November 26th 2011, 09:04 PM

At age 66, your grandson will have $161,564.30.

I'm not an expert, but don't forget inflation in whatever balances you want to do. In other words, $161,564.30 might seem good from today's perspective but 66 years from now it might not be so...

**Soroban** · November 27th 2011, 09:13 AM

Hello, agooolka!

Question #2; Assume you had saved $35.00 a month since you were 18 years old.
When you got to be 70, the age at which you must begin withdrawing all retirement plans,
how much money would you end with?

We need to know the annual interest rate.

Question #3; Assume you had a very wonderful granddad. .When you were born,
he wanted you to have an investment plan that would give you $1,000,000.
So, he set it up and he invested until you turned 18.
Then, it was your duty to continue the investment.
He wanted you to have $1,000,000 when you turned 70.
Assume the best average interest rate for the period is 7%.
what is the amount of monthly deposit that would be required?

At age 18, you would have $P$ dollars.
You invest this at 7% compouned monthly for the next 52 years,
. . and you want to receive $1,000,000.

We have: . $P\left(1 + \tfrac{0.07}{12}\right)^{624} \:=\:1,\!000,\!000$

. . Then: . $P \:=\:\frac{1,\!000,\!000}{(1 + \frac{0.07}{12})^{624}} \:=\:26,\!531.45045$

You must have $26,531.45 at age 18.

The annuity formula is: . $A \:=\:D\,\frac{(1+i)^n-1}{i}$

. . $\text{Solve for }D\!:\;\;D \;=\;\frac{Ai}{(1+i)^n-1}$

We have: . $D \;=\;\frac{(26,531.45)(\frac{0.07}{12})}{(1 + \frac{0.07}{12})^{216} -1} \;=\;61.59775902$

Your grandfather must deposit $61.60 monthly for your first 18 years.

**agooolka** · November 27th 2011, 09:05 PM

It's 5% interest

Thanks for the help!

**Soroban** · November 30th 2011, 07:40 AM

Hello again, agooolka!

Question #2. Assume you had saved $35.00 a month since you were 18 years old.
When you got to be age 70, how much money would have? .Interest rate is 5%.

I'm sorry, but I must ask . . .
Why are you having trouble with this one?
It is the easiest of the three questions.

The periodic depoist is $35.
The monthly interest rate is $\tfrac{0.05}{12}$
The number of periods is $52\cdot 12 \,=\,624$ months.

We have: . $\begin{Bmatrix}D &=& 35 \\ i &=& \frac{0.05}{12} \\ n &=& 624\end{Bmatrix}$

Substitute into the formula: . $A \;=\;D\,\frac{(1+i)^n-1}{i}$

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