Annual equal installments

[nitdhe]

What annual payment will discharge a debt of Rs. 440 due in 5 years at simple interest reckoned at 5 %


X = 100 * P * (Y) / 100 T + { RT ( T – 1 ) /2}

X = 100 * 440 * (1) / 100 * 5 + { 5*5 ( 5 – 1 ) /2}

X = Rs 80.

I can’t understand the formula
Please give me the explanation for the above formula.

I am frustrated with this problem plz plz help me for this problem

Thank you .

 

[Deleted member 4993]

What annual payment will discharge a debt of Rs. 440 due in 5 years at simple interest reckoned at 5 %


X = 100 * P * (Y) / 100 T + { RT ( T – 1 ) /2}

X = 100 * 440 * (1) / 100 * 5 + { 5*5 ( 5 – 1 ) /2}

X = Rs 80.

I can’t understand the formula
Please give me the explanation for the above formula.

I am frustrated with this problem plz plz help me for this problem

Thank you .

What are the meaning of those variable?

Something wrong with your example (or my interpretation). You end-up paying Rs. 400 after 5 years for a debt of 440 - less than the original amount??

 

[nitdhe]

Thank you sir for replying me.

What annual payment will discharge a debt of Rs. 440 due in 5 years at simple interest reckoned at 5 %


X = 100 * P * (Y) / 100 T + { RT ( T – 1 ) /2}

X = 100 * 440 * (1) / 100 * 5 + { 5*5 ( 5 – 1 ) /2}

X = Rs 80.


Meanings of the variables

X = Annual equal installment
P = Debt
T = Time
R = Interest Rate
Y = 1 for yearly installment
Y = 2 for half yearly installment

 

[tkhunny]

It would be simpler if we could just pay off the interest and cancel the loan at the end with a Rs 440 balloon. You have insisted on equal annual installments. This is a nice complication. It challenges the definition of "Simple Interest". Really, though, we just have to think one year at a time.

Loan is 440.
Annual Payment is P
Interest it 5%
Accumulation factor for one year is 1.05

440*1.05 - P = Still owing at the end of one year. Obviously, P > 440*0.05 = 22 and we pay off some principal at this time.

(440*1.05 - P)1.05 - P = Still owing at the end of two years.

((440*1.05 - P)1.05 - P)1.05 - P = Still owing at the end of three years.

(((440*1.05 - P)1.05 - P)1.05 - P)1.05 - P = Still owing at the end of four years.

((((440*1.05 - P)1.05 - P)1.05 - P)1.05 - P)1.05 - P = 0 = Still owing at the end of five years.

A little algebra

440*1.05^5 - P(1.05^4 + 1.05^3 + 1.05^2 + 1.05 + 1) = 0

More algebra

440*1.05^5 - P(1.05^5 - 1)/(0.05) = 0

Are we getting anywhere?

 

[Denis]

X = 100 * P * (Y) / 100 T + { RT ( T – 1 ) /2}

Where d'heck did you get that weirdo formula?

Formula is:
P(ayment) = Ai / (1 - x) where x = 1 / (1 + i)^n

A = Amount borrowed (440)
i = interest rate (.05)
n = number years (5)

So annual payment = 440(.05) / (1 - x) where x = 1 / (1.05)^5

 

[tkhunny]

...again begging the question about how "Simple" the interest is.

 

[Deleted member 4993]

I guess, it is not compounding quarterly or monthly - where as the payment is yearly.

Of course, as you suggested, the wording is confusing.

 

[Denis]

...again begging the question about how "Simple" the interest is.

I always "took it" that unless otherwise specified, simple interest
meant no compounding during the year, but compounding at year ends.

I think you mean no compounding at any time, right TK? So required payment = 100:

00                   440.00
01 -100              340.00  22.00  22.00
02 -100              240.00  17.00  39.00
03 -100              140.00  12.00  51.00
04 -100               40.00   7.00  58.00
05 -100  + 60.00        .00   2.00  60.00

Last 2 colums shows the interest accumulating without being compounded.

I worked out this funny looking formula to get the payment P:

P = 2A(x + 1) / [2n + x(n - 1)] where x = ni

A = Amount borrowed (440)
n = number of years (5)
i = interest rate (.05)

Do you know of a "standard" one?

 

[tkhunny]

Or

$440*0.05*5 = $110

$440+$110 = $550

$550/5 = $110

What, exactly, does "due in 5 years" mean?

The World is confused on this point. I know of no standard, anywhere. Contract terms, and problem statements, must be worded VERY CAREFULLY. The student should specify assumptions with lucidity. Recognizing that they are assumptions is the important part. It is the very, very unusual consumer who can calculate a loan payoff with acceptable precision.