A customer walks into a Bank with $100,000. He wishes to buy 5 CD's (Cetificates of Deposit) for 5 years as follows:
1-year CD that pays 3% compounded semi-annually.
2-year CD that pays 4% .............................................
3-year CD that pays 5%..............................................
4-year CD that pays 6%..............................................
5-year CD that pays 7%..............................................
The questions: a-How much must he deposit in each CD, that ALL 5 CD's will have exactly the same amount at maturity, thereby, effectively receiving 5 equal-amount annuity payments for his initial deposit of $100,000. b- What would the effective annual rate of return on his "annuity" be for the 5 years? Good luck to all.
I'm just gonna guess 3 + 4 + 5 + 6 + 7 = 25
3/25 x 100k in the 7 % account
4/25 x 100k in the 6% account
5/25 x 100k in the 5% account
6/25 x 100k in the 4% account
7/25 x 100k in the 3% account
Just a quick guess...I don't feel like ACTUALLY figuring it out....
Guest #1
Sorry! That is NOT going to work. Why? Remember, each CD cannot be more than $100,000/5=$25,000. Your last part of 7/25 X 100,000=$28,000?????.
+118724 A customer walks into a Bank with $100,000. He wishes to buy 5 CD's (Cetificates of Deposit) for 5 years as follows:
The questions: a-How much must he deposit in each CD, that ALL 5 CD's will have exactly the same amount at maturity, thereby, effectively receiving 5 equal-amount annuity payments for his initial deposit of $100,000. b- What would the effective annual rate of return on his "annuity" be for the 5 years? Good luck to all.
1-year CD that pays 3% compounded semi-annually. $22,811.55
2-year CD that pays 4% ............................................. $21,711.32
3-year CD that pays 5%.............................................. $20,264.86
4-year CD that pays 6%.............................................. $18,551.93
5-year CD that pays 7%.............................................. $16,660.32
The customer can pocket the other 2c
Yearly 'annuity' = $23,501.03
Excellent Melody!. Five stars from me. Do you think you can figure out the annual rate of return on his "annuity"? Thanks for great effort.
Bravo!!. I would give you 10 stars if only I knew how to do that!!!!!!.
True. I worked as an "Investments Banker"!!!.
Guest #1 .... you never said the deposits could not be greater than 100000/5 ! In fact , the answer requires it ! D'oh!
Sorry, I meant to say the "average". Given that, try and see if you can get the answers that Melody got. But, you must give the methods used. Good luck.
I had to sleep on this last night, but I came up with this answer:
x1 = Amount invested at 3%
x2= Amount invested at $%
etc.
We know Present Value + 100,00 BUT we do NOT know what the Future value will be...BUT we do know they will all be equal....
x1(1.015)^10 = x2 (1.020)^10 = x3 (1.025)^10 etc
SO we need to equate all of the Future Values bact to the Present and express them in terms of x1 Like this
x2 = x1(1.105)^10/(1.020^10) for all of the terms.....then add them all together , equate them to 100000 and solve for x1 etv
Here is what results (to the PENNY):
x1 (3%) =22,002.49
x2(4%) =20,947.42
x3(5%) =19947.73
x4(6%) =19000.28
x5(7%) = 18102.09
It involved a lot of power of ten fractions that had to be calculated.....thanx for calculators with memories!!!!
The final value of each cd will be equa @ 25534.78 for a total of 127673.90
TaDa! Fun !
~jc
Nice try jc!!!!. Unfortunately for you, it is wrong!. Look at the numbers that Melody has calculated. That is the right answer to the penny!
But I just tried Melody's answers ...and they are not equal at the end of th Five year period?
Look at her 3% value at the end of five years it will be 22811.55 (1.015)^10 = 26473.73
then look at the 7% one 16660.32 (1.035)^10 = 23502.43 They are not equal? Am I mireading the question?
I thought the neding values were supposed to be equal.......Did I miss calculate? If you do these calcs with my numbers, the ending values are all equal.....What did I do wrong? AM I wrong????
~jc
jc: I don't think you understand the problem!. Each CD that he/she purchased at the amounts calculated by Melody will mature with exactly the same amount, which is $23,501.03. That is what an "annuity" is.
This person could have easily gone to an Insurance Company and purchased a 5-year annuity, with equal payments being sent to him/her. If the Insurance Co. agreed and told him/her that they would receive 5 payments each for $23,501.03, then that would be exactly like this investment.
OK, jc: I think I know what you did wrong. Look below:
1-year CD that pays 3% compounded semi-annually. $22,811.55 X (1.015)^2=$23,501.03
2-year CD that pays 4% ............................................. $21,711.32 X (1.02)^4 =same amount
3-year CD that pays 5%.............................................. $20,264.86 X (1.025)6 =same amount
4-year CD that pays 6%.............................................. $18,551.93 X (1.03)^8 =same amount
5-year CD that pays 7%.............................................. $16,660.32 X (1.035)^10=same amount
Oh CRUD ! D'oh! I just CAREFULLY re-read the quesstion.... I had ALL of the CDs as FIVE year CDs......jeez. I had the right methodology at least, just the wrong inputs. Computers do not give you correct answers if you give them the wrong data!
Way to go Melody! ~jc
Thanx for your repeated help on this......thought I was going nutz ....or Deez Nutz as the case may be..... ha
~jc
