Question 1193369: Kindly requesting your help about homework.
1.Mr farmer needs to make the following payments against a loan on his truck:R10000 after 6 months, R20000 after 1 year,R40000 after 2 years.Due to drought he could not make the first two payments. After 18 months Mr farmer make the down payment of R50000 against the loan.
1.1. Draw a timeline to represent the above mentioned scenario.
1.2. What single payment should he make two years from now to settle his debt if a simple interest rate of 17% is applied on all the amounts.
Found 2 solutions by ElectricPavlov, ikleyn:
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **1.1. Timeline**
The timeline for Mr. Farmer's loan payments is as follows:
* 0 months: Loan Disbursement
* 6 months: Payment of R10000 due (missed)
* 12 months: Payment of R20000 due (missed)
* 18 months: Payment of R50000 made
* 24 months: Payment of R40000 due
* 36 months: Single payment due
**1.2. Single Payment Calculation**
To calculate the single payment Mr. Farmer needs to make in two years (36 months) to settle his debt, we need to consider the following:
* **Accumulated debt at 18 months:** This includes the missed payments, interest on those missed payments, and the remaining loan balance after the R50000 down payment.
* **Future value of the accumulated debt at 36 months:** We need to factor in the interest that will accrue on the accumulated debt over the additional 18 months.
* **Future value of the R40000 payment at 36 months:** The R40000 payment is also due in two years, so we need to calculate its future value considering the interest.
* **Single payment:** The sum of the future value of the accumulated debt and the future value of the R40000 payment will be the total amount Mr. Farmer needs to pay.
**Calculations:**
* Let's assume a simple interest rate of 17%.
* **Payment 1 Interest:** 10000 Rand * (17% interest rate) * (18 months / 12 months) = 2850 Rand
* **Payment 2 Interest:** 20000 Rand * (17% interest rate) * (12 months / 12 months) = 3400 Rand
* **Accumulated debt at 18 months:** 10000 Rand (original payment) + 2850 Rand (interest on payment 1) + 20000 Rand (original payment 2) + 3400 Rand (interest on payment 2) - 50000 Rand (down payment) = -14050 Rand (negative value indicates Mr. Farmer still owes money)
* **Future value of accumulated debt at 36 months:** -14050 Rand * (1 + 17% interest rate * (18 months / 12 months)) = -17632.75 Rand
* **Future value of R40000 payment at 36 months:** 40000 Rand * (1 + 17% interest rate * (12 months / 12 months)) = 46800.00 Rand
* **Single payment due at 36 months:** -17632.75 Rand + 46800.00 Rand = 29167.25 Rand
**Answer:**
Therefore, Mr. Farmer needs to make a single payment of R29167.25 in two years (36 months) to settle his debt. This amount considers the accumulated debt, interest on missed payments, and the future value of the R40000 payment due at that time.
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
Please help me with the homework.
1. Mr farmer needs to make the following payments against a loan on his truck:
10000 after six months, 20000 after one year, 40000 after two years.
Due to drought, he could not make the first two payments.
After 18 months, Mr farmer immediately make a down payment of 50000 against the loan.
1.1. Draw a timeline to represent the above mentioned scenario
1.2. What single payment should he make two years from now to settle his debt
if a simple interest rate of 17% is applied on all the amounts.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I believe that
"10000 after six months, 20000 after one year, 40000 after two years"
in the post means
"10000 six months from now, 20000 one year from now, 40000 two years from now."
I do not agree with the post by @ElectricPavlov - neither with their conception, nor with their calculations.
Below I present my conception, my calculations and my solution, with the answer.
After my solution, I presented the @ElectricPavlov writing with my comments.
S O L U T I O N
**1.1. Timeline**
Here's a simple representation of the timeline:
0 months:** Loan Disbursement
6 months:** Payment of R10,000 due (missed)
12 months:** Payment of R20,000 due (missed)
18 months:** Down payment of R50,000 made
24 months:** Payment of R40,000 due, and the farmer makes his last payment to settle his debt.
**1.2. Single Payment Calculation**
(a) His accumulated debt "after 18 months from now" is
base the interest base the interest
scheduled accrued scheduled accrued
payment for not paid amount payment for not paid amount
not paid "after 18 months from now" not paid "after 18 months from now"
at the time 18-6 = 12 months overdue at the time 18-12 = 6 months overdue
against the schedule against the schedule
10000 + 10000*(18-6)*(0.17/12) + 20000 + 20000*(18-12)*(0.17/12) = 33400.
(b) The balance "at 18 months from now" after paying 50000 against the loan is
33400 - 50000 = -16600, so the farmer is now ahead of his schedule.
(!) Now THE BANK owes 16600 to the farmer.
The problem does not describe what the bank does in this situation.
So, at this point I should stop in bewilderment (formally).
OK, let's assume that the bank makes nothing, so the farmer's money (16600) lie
and wait "to 24 months from now" with no change.
(c) Then the single payment "24 months from now" is 40000 - 16600 = 23400. ANSWER
Solved.
=======================
Below I placed the tutor's @ElectricPavlov calculations with my comments.
To calculate the single payment Mr. Farmer needs to make in two years (24 months) from now to settle his debt, we need to consider the following:
* **Accumulated debt at 18 months:** This includes the missed payments, interest on those missed payments, and the remaining loan balance after the R50,000 down payment.
* **Future value of the accumulated debt at 24 months:** We need to factor in the interest that will accrue on the accumulated debt over the additional 6 months.
* **Future value of the R40,000 payment at 36 months:** The R40,000 payment is also due in two years, so we need to calculate its future value considering the interest.
* **Single payment:** The sum of the future value of the accumulated debt and the future value of the R40,000 payment will be the total amount Mr. Farmer needs to pay.
**Calculations:**
* **Payment 1 Interest:** 10,000 Rand * (17% interest rate) * (18 months / 12 months) = 2,550 Rand
why 18 months here? - should be 12 months overdue. The number of 2,550 is wrong.
* **Payment 2 Interest:** 20,000 Rand * (17% interest rate) * (12 months / 12 months) = 3,400 Rand
why 12 months here? - should be 6 months overdue. The number of 3,400 is wrong.
* **Accumulated debt at 18 months:** 10,000 Rand (original payment) + 2,550 Rand (interest on payment 1) + 20,000 Rand (original payment 2) + 3,400 Rand (interest on payment 2) - 50,000
from what precedes, these numbers are wrong
Rand (down payment) = -14,050 Rand (negative value indicates Mr. Farmer still owes money)
* **Future value of accumulated debt at 36 months:** -14,050 Rand * (1 + 17% interest rate * (18 months / 12 months)) = -17,632.75 Rand
wrong interpretation: mr farmer is AHEAD of the schedule - so, the BANK owes money to mr. farmer.
* **Future value of R40,000 payment at 36 months:** 40,000 Rand * (1 + 17% interest rate * (12 months / 12 months)) = 46,800.00 Rand
Why 12 months interest is calculated and added ? - It is wrong.
* **Single payment due at 36 months:** -17,632.75 Rand + 46,800.00 Rand = 29,167.25 Rand
The calculations are incorrect and the answer is wrong.
**Therefore:**
Mr. Farmer needs to make a single payment of **R29,167.25** in two years (36 months) to settle his debt. This amount considers the accumulated debt, interest on missed payments, and the future value of the R40,000 payment due at that time.
This answer is wrong.
The calculations in the post by @ElectricPavlov are not consistent and contradict to their TimeLine.
As I see from this post, the other tutor (which is an AI, I believe) 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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