Question 1193511: Please help me with the homework.
Mr farmer needs to make the following payments against a loan on his truck:
R10000 after 6months, R20000 after 1 year, R40000 after 2 years.After 18 months, Mr farmer had a record harvest and immediately makes a down payment of R50000 against 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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe i have it.
once you understand what's going on, it's not really all that difficult.
it is a little tricky getting to the point of understanding though, as i found out when working with this problem.
here's what i got.
formula for simple interest loan is f = p * (1 + r * t)
f is the future value.
p is the present value which also called the principal.
r is the interest rate per year.
t is the number of years.
in a simple interest loan, the interest is calculated up front and then added to the principal.
that becomes the total amount due at the end of the loan period.
the payments are then calculated to add up to the total value of the loan at the end of the loan period.
the total payments of the loan were 10,000 + 20,000 + 40,000 = 70,000.
since the sum of these payments had to be enough to satisfy the loan, then the 70,000 is equal to the future value of the loan.
the interest rate per year is 17% = .17
the number of years of the loan is 2.
the formula becomes:
70,000 = p * (1 + .17 * 2)
solve for p to get:
p = 70,000 / (1 + .17 * 2) = 52238.80597.
that's the present value of the loan which is the principal amount of the loan as well.
the payment schedule can be anything you want it to be as long as the sum of the payments is 70,000 and all payments are made by the end of the loan period.
since 50,000 was paid 18 months from the start of the loan, the remaining payments had to be 20,000, because of the above statement that said that the schedule could be anything as long as the sum of the payments was 70,000.
i followed that logic and it turned out to be true.
i had to calculate the total interest of the loan.
that was
the following excel spreadsheet shows that.
that was the present value of the loan * .17 * 2 which became:
52238.80597 * .17 * 2 = 17761.19403.
that could also have been determined as 70,000 - 52238.80597 = 17761.19403.
this total interest was divided by 4 half years to make it equal to 4440.298508 per each half year.
the first part of the display is the original payment schedule.
you can see that the remaining balance of the loan is 0 at the end of the loan period.
the second part of the display replaces all payments with 50,000 in 18 months.
you can see that 20,000 is still owed at the end of the loan period.
the third part of the display adds a payment of 20,000 at the end of the second year.
you can see that the remaining balance is again 0 at the end of the loan period.
as long as the sum of the payments was 70,000, the loan was satisfied by the end of the loan period.
i'm pretty sure this is the correct way to look at it, but i always allow that i could be wrong.
if, in fact, my assumptions about how the solution to the problem works are wrong, than the solution will most likely be wrong as well.
see if this works for you.
let me know how you did and if you have any questions regarding it.
theo
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