Twins graduate from a college together and starts their carrier. Twin 1 invest $2000 at the end of each month of 8 years in an account that earns 10% compounded annually .after the initial 8 years no additional contribution are made but the investement continues to earn 10% compound annually . Twins 2 invest no money for 8 years but then contributes $ 2000 at the end of each year for a period of 36 years (to age 65) to an account that pays 10% compounded annually . 1) How much money does each twin contributes .? 2) How much money does each twin have at the age of 65? 3) If you are supposed to choose one of those scheme which will you choose explain.
Answers
Answer:
Twins graduate from college together and start their careers. Twin 1 invests $2500 at the end of each year for 10 years only (until age 31) in an account that earns 6%, compounded annually. Suppose that twin 2 waits until turning 40 to begin investing. How much must twin 2 put aside at the end of each year for the next 25 years in an account that earns 6% compounded annually in order to have the same amount as twin 1 at the end of these 25 years (when they turn 65)? (Round your answer to the nearest cent.)
I have attempted the solution as follows, but it is wrong. Can you please tell me where my work is off?
Twin I
First 10 years (Age 20-30)
PV = 0
Int = 6%
Pmt = $2,500
Solve for FV = $32,951.99
Last 35 years (Age 31-65)
PV = $32,951,99
Pmt = $0
Int = 6%
Solve for FV = $253,271.86
Twin II
PV = $0
Int = 6%
FV = $253,271,86
N= 25 years (age 41-65)
Solve for Pmt = $4,616.31
The $4,616.31 answer is incorrect. My only thought is that I should be starting Twin I at 21 years of age, which would drop the second part of that Twin I answer N value from 35 years (65 yrs - 30 yrs) to 34 years (65 yrs - 31 yrs). I think that would drop the FV for twin I to $239,935.71, and the Pmt for Twin II to 4,355.01. Is that the error here?
Any assistance is appreciated.
Answer by greenestamps(9290) (Show Source): You can put this solution on YOUR website!
I get all the same numbers as you, within a few cents.
Do you know if the answer you got by changing from 35 years to 34 years is the right answer? That's the answer I get.
I think the 34 is the right number to use, because each of them is making the contributions at the end of each year. If the first twin started investing at age 21 and made contributions for 10 years, then he is 31 when he stops making contributions; it is then 34 more years to when he is 65.
RELATED QUESTIONS
Given:
Twin 1 invests $2000 at the end of each month for 8 years.
Twin 2 invests no money for 8 years but afterwards contributes $2000 at the end of each year for a period of 36 years.
Rate of interest = 10%
It is compounded annually.
To Find:
a) Amount that each twin contributes.
b) The amount each twin has at the age of 65.
c) Which scheme will you choose?
Solution:
We can simply solve this problem by using the following mathematical process.
a) Twin 1 invests $2000 at the end of each month for 8 years.
Therefore, the period of investment = 8 × 12
And,
Total amount invested = 8 × 12 × 2000
$1,92,000
Twin 2 invests $2000 for 36 years at the end of each year.
So,
Total amount invested = 36 × 2000
$72,000
b) Using the formula for compound interest i.e.
For twin 1, for the first 8 years
C.I. = $274,461.31
Last 36 years,
C.I. = $8,484,334.79
Total C.I. = $87,58,796.1
This will be the amount when twin 1 turns 65.
For twin 2,
C.I. = $598,265.58
This will be the amount when twin 2 turns 65.
c) Scheme 1 should be chosen to earn more as it will give a much better return.
Hence, the correct answers are given in each part.
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