Question 1193455: Julita owes Jose the following amounts:
a. 55,000 at the end of 4 years,
b. 48,000 at the end of 5 years, and
c. 75,000 due in 3 years from today at 9% converted quarterly.
What single payment at the end of 2 years will settle Julita’s
obligations if money is worth 15% converted monthly?
Found 2 solutions by yurtman, ikleyn:
Answer by yurtman(42)   (Show Source):
You can put this solution on YOUR website! **1. Calculate the Present Value of Each Obligation:**
* **Obligation 1:**
* Present Value (PV1) = 55,000 / (1 + 0.15/12)^(4*12)
* PV1 = 55,000 / (1.0125)^48
* PV1 ≈ 26,534.62
* **Obligation 2:**
* Present Value (PV2) = 48,000 / (1 + 0.15/12)^(5*12)
* PV2 = 48,000 / (1.0125)^60
* PV2 ≈ 19,737.68
* **Obligation 3:**
* Quarterly interest rate for Obligation 3: 0.09 / 4 = 0.0225
* PV of Obligation 3 at the end of 3 years: 75,000 / (1 + 0.0225)^(3*4) = 75,000 / (1.0225)^12
* PV of Obligation 3 at the end of 3 years: ≈ 57,096.79
* Present Value (PV3) = 57,096.79 / (1 + 0.15/12)^(3*12)
* PV3 = 57,096.79 / (1.0125)^36
* PV3 ≈ 35,320.95
**2. Calculate the Total Present Value of All Obligations**
* Total Present Value (Total PV) = PV1 + PV2 + PV3
* Total PV = 26,534.62 + 19,737.68 + 35,320.95
* Total PV ≈ 81,593.25
**3. Calculate the Single Payment at the End of 2 Years**
* Single Payment = Total PV * (1 + 0.15/12)^(2*12)
* Single Payment = 81,593.25 * (1.0125)^24
* Single Payment ≈ 120,984.66
**Therefore, a single payment of approximately 120,984.66 at the end of 2 years will settle Julita's obligations.**
Answer by ikleyn(52792)  (Show Source):
You can put this solution on YOUR website! .
Julita owes Jose the following amounts:
a. 55,000 at the end of 4 years,
b. 48,000 at the end of 5 years, and
c. 75,000 due in 3 years from today at 9%  compounded quarterly.
What single payment at the end of 2 years will settle Julita’s
obligations if money is worth 15% compounded monthly?
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Calculations in the post by @yurtman all are incorrect.
They are incorrect technically, since he uses incorrect effective growth factors everywhere.
They are incorrect conceptually, since his solution is conceptually incorrect.
In this problem, as it is worded, 15% compounded monthly is irrelevant data,
which should not be used in the solution.
Regarding the problem itself, as worded in the post, it is soup of words with no sense.
To make sense from nonsense, the problem should be re-written/re-formulated this way:
Julita owes Jose the following amounts:
(a) 55,000 at the end of 4 years,
(b) 48,000 at the end of 5 years, and
(c) 75,000 at the end of 3 years.
Jose has an account in the bank, which pays 9% annually compounded quarterly.
Therefore, Jose agrees to accept a single payment from Julita at the end of 2 years
to deposit it to this account and to settle Julita's obligations this way.
What amount should pay Julita to Jose in 2 years from now ?
I came to bring a correct solution to this re-formulated problem.
In this problem, we should calculate the value of the debt at the end of the two years from today.
It is all what should be calculated, since this value represents the obligation at the end of 2 years.
1. Calculate the value of each obligation at the end of 2 years from now:
Obligation 1 at the end of 2 years from now (rewind two years back from 4 years)
Value = 55000 / (1 + 0.09/4)^(2*4)
Value = 46031.61
Obligation 2 at the end of 2 years from now (rewind three years back from 5 years)
Value = 48000 / (1 + 0.09/4)^(3*4)
Value = 36752.04
Obligation 3 at the end of 2 years from now (rewind one year back from 3 years)
Value = 75,000 / (1 + 0.09/4)^(1*4)
Value = 68613.25
2. Calculate the Total of All Obligations two years from now
Total of the three obligations: 46031.61 + 36752.04 + 68613.25 = 151396.90
ANSWER. The single payment of 151396.90 will settle Julita's obligations at the end of 2 years from now.
Solved.
Regarding the post by @yourtman (which is an AI, I believe), I see that it/he is not able to establish
right strategy of solution and is not able to produce calculations correctly.
It works following the principle "to generate as many words as possible, hoping that
nobody will even try to figure out if it is correct".
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To the managers of this project
On your side, you have a person - the problem's composer/creator - who produces
half-non-sensical writing and disseminate it in the Internet.
This person definitely does not understand what he writes.
Take all necessary measures to keep the project in order.
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