In five years, you plan on starting graduate school to earn your MBA. You know t
ID: 2652686 • Letter: I
Question
In five years, you plan on starting graduate school to earn your MBA. You know that graduate school can be expensive and you expect you will need $15,000 per year for tuition and other school expenses. These payments will be made at the BEGINNING of the school year. To have enough money to attend graduate school, you decide to start saving TODAY by investing in a money market fund that pays 4% APR with monthly compounding. You will make monthly deposits into the account starting TODAY for the next five years. How much will you need to deposit each month to have enough savings for graduate school? (Assume that money that is not withdrawn remains in the account during graduate school and the MBA will take two years to complete.)
Explanation / Answer
We have nominal rate = 4% APR compounded monthly
Effective Rate = (1+.04/12)12-1
= 4.0742%
Required present value of tution and other school payments i.e.
First Payment will be required at the begining of 6th Year or at the end of 5th year i.e. $15,000
Second payment of $15,000 will be required at the begining of 7th year or at the end of 6th year i.e. we will have to compute present value at the end of 5th year
Now the total payment required at the end of 5th year is as follows:
PV = $15,000 + $15,000 /(1+0.40742)
= $15000 + $14412.79
= $29,412.80
Now we require the amount of saving each month so that we will get $29,412.80
N = no. of periods = 60
i = Nominal rate of Interest = 4%/12 = 0.003333
A = amount of annuity / saving each month
FV = Future value needed = $29,412.80
Formula of Future Value of an annuity
FV = A x [(1+i)n-1/i]
= $29412.80 = A x [ (1+0.003333)60-1/0.003333]
= $29412.80 = A x [ 1.22097 - 1/ 0.003333 ]
= A = $29412.80/66.2983
= $443.64
If we invest $443.64 every month for 5 year, we will get an amount of $29412.80
Note: Exact answer is $442.16. Difference is due to rounding off. If calculations are done through financial calculator or approxiamation is increased then the differnce will be nil.