Uhdam would like to save $80,000 for a deposit on her first home.She has decided to invest her net monthly salary of $4500 at the beginning of each month .
she earns 4.5% in interest per annum, compounded monthly. Uhdam intends to $M at the end of each month from her account for living expenses, immediately after the interest has been paid.
i) show that the amount of money at the end of the 2nd month following the second withdrawel of $M is given by:
$4500 (R2+R)-$M(R+1), where R=1+ 4.5/1200
ii) If Uhdam is to reach her goal in 6 years , show that
M=(4500(R72+R71+⋯+R)-80000)/(R71+R70+⋯+R+1)
iii) calculate the value of M. Leave your answer to the nearest integer
Can any of you guys decipher this investment question? Let us see who is brave enough to tackle it!!.
Wow!. Is this a "Challenge Question" or what??.
First, the person or the teacher who posed this question doesn't seem to be familiar with modern TVM formulas!!
There are two questions here:
1) What is the amount of $M that she can withdraw each month and still allow her to save $80,000 as a down payment on her house?.
We know she deposits $4,500 in her savings account that earns 4.5% comp. monthly.
Will have to find the FV of these 72 payments (6 years) using this common formula:
FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
Plugging all the numbers in and crunching them, we get:
FV=$372,555.59. But we know she wants to keep $80,000 of this for her down payment. So we have:
$372,555.59 - $80,000 =$292,555.59 the balance in savings account that she can spend.
Plugging this into the above TVM formula, we can calculate her monthly withdrawal from her savings account. And this monthly amount comes to:$3,533.70. This is the amount of $M in the question.
2) The balance in her savings account after depositing two payments of $4,500 each and withdrawing of two payments of $3,533.70 each will be:
$9,050.69 - $7,107.20=$1,943.48, using the same above TVM formula!!.
P.S. The two questions posed were answered in reverse, in order to determine the $M of her withrawals. Also, remember that her payments were made at the beginning of the month, which has been taken into account. All that mumbo-jumbo of R^72+R^71+R^70.........are totally unnecessary. And that is the END!!.
