When Suzie was born, her Grandmother decided to set up an educational fund for her granddaughter college education. It is assumed that Suzie would start her college education at 18. The fund was planned in such a way as to have sufficient funds in it to pay the college an annual tuition fee of $30,000 at the beginning of each year for 4 years. In addition, the fund would permit Suzie to withdraw $1,000 at the beginning of each month for her living expenses. How much money would Suzie's Grandmother have to deposit each month in her fund to meet her granddaughter's college expenses, if the interest rate is assumed to be 5% compounded monthly.
+118609 There are many parts to this question so I will just talk about it for a bit.
The interet rate stays set at 5% pa compounded monthly.
this is 0.05/12 = 0.00416666666666
You need to work out how much money you will need in the accout on Suzie's 18 birtday., there are 2 parts to this.
1) Suzzie will need $1000 at the beginning of each month for 4 years and you need to know how much this equates to on her 18th birthday.
You can do this as the present value of an annuity due problem.
r=0.00416666666666
n=48
M=1000
2) You also need to work out what $30000 at the beginning of each year for 4 years equates to.
Before you can do this you need to work out what the effective interest rate of 0.00416666666666 per month is per year.
Solve this to get the answer. 1.00416666666666^12=1+R
Then
Use the present value of an annuity due formula using this new R, n=4, M=30000.
I'll call this total A18
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3) Add those answers together and you will know how much money you need by the 18th birthday.
4) Gran deposits X amount of dollars at the beginnig of every month for 12*18= 216 months
and at the end of it her Future value of an annuity due total will be equal to A18
Maybe you can use this outline to work the answer out for yourself.
Good luck :)
Dear Guest,
I honestly don't want to do math. You may wonder why I'm on, it is a great way to pass time when babysitting. Looool! And I am not a bad babysitter. The kid fell asleep watching TV on the sofa. XD
+118609 I assume the grandmother made the first depsoit the day the child was born.
Then she made monthly deposits.
When did she stop making monthly deposits?
My book doesn't say! But assume each month for 18 years until Suzie's 18th birthday.
+118609 There are many parts to this question so I will just talk about it for a bit.
The interet rate stays set at 5% pa compounded monthly.
this is 0.05/12 = 0.00416666666666
You need to work out how much money you will need in the accout on Suzie's 18 birtday., there are 2 parts to this.
1) Suzzie will need $1000 at the beginning of each month for 4 years and you need to know how much this equates to on her 18th birthday.
You can do this as the present value of an annuity due problem.
r=0.00416666666666
n=48
M=1000
2) You also need to work out what $30000 at the beginning of each year for 4 years equates to.
Before you can do this you need to work out what the effective interest rate of 0.00416666666666 per month is per year.
Solve this to get the answer. 1.00416666666666^12=1+R
Then
Use the present value of an annuity due formula using this new R, n=4, M=30000.
I'll call this total A18
------------------------------------------------------
3) Add those answers together and you will know how much money you need by the 18th birthday.
4) Gran deposits X amount of dollars at the beginnig of every month for 12*18= 216 months
and at the end of it her Future value of an annuity due total will be equal to A18
Maybe you can use this outline to work the answer out for yourself.
Good luck :)
