Confirm Interest Rate Solution on Total Loan

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Discussion Overview

The discussion revolves around a problem involving simple interest calculations related to a loan taken by a small firm. Participants are attempting to determine how much additional money the firm borrowed from a company secretary and what the overall interest rate on the total loan is, based on the total repayment amount after one year.

Discussion Character

  • Mathematical reasoning
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant proposes a calculation method to find the additional money lent by the secretary and the total interest rate, leading to a conclusion of \$47,548.48 as the additional amount and an interest rate of 8.23% on the total loan.
  • Another participant challenges the correctness of the initial calculations, suggesting that the equations set up do not properly represent the relationship between total repayment and interest accrued.
  • Several participants express confusion and request assistance in solving the problem, indicating a lack of clarity in the calculations presented.
  • Another participant suggests an alternative solution, stating that the additional money lent is \$2,700 and the total amount is \$3,700, proposing an interest rate of 8% for the total loan.
  • A later reply agrees with the alternative solution but provides a slightly different interest rate of 8.047%.
  • Some posts diverge into unrelated humor, which detracts from the mathematical focus of the discussion.

Areas of Agreement / Disagreement

There is no consensus on the correct solution to the problem. Multiple competing views and calculations are presented, leading to disagreement among participants regarding the correct amounts and interest rates.

Contextual Notes

Participants' calculations depend on the interpretation of the relationship between total repayment, principal, and interest. There are unresolved mathematical steps and assumptions that may affect the conclusions drawn.

bergausstein
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A small firm borrows \$1000 from a stockholder at a sim-pleinterest rate of 7.5%. The company secretary lends the firm an additional sum at a simple interest rate of
8.25%. At the end of one year, the firm repays a total of
\$3997.75. How much did the secretary lend the firm and
what is the simple interest rate on the total loan?

let

$y=$ additional money lent

$1000+y =$ total amount of money lent.

$1000(0.075)+0.0825y=3997.75$

$0.0825y=3997.75-75$

$y=47,548.48$ - additional money lent.

$1000+47,548.84 = 48548.48$ total amount of money lent.

$\frac{3997.75}{48548.48}=0.823=8.23\%$ interest rate on the total loan.i just want to confirm if my solution is correct. thanks!
 
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Re: ALGEBRA Profit problem.

look at the below quotes carefully,
the firm repays a total of $3997.75.
48548.48 total amount of money lent
$$1000(0.075)+0.0825y=3997.75$$
 
Re: ALGEBRA Profit problem.

it's not correct!:)
 
Last edited:
Re: ALGEBRA Profit problem.

i can't figure it out. please help.
 
Re: ALGEBRA Profit problem.

bergausstein said:
i can't figure it out. please help.
Hello.

Stockholder: 1000.00

Interest stockholder:\ 1000.00*0.075=75.00

Secretary= x

Interest secretary= 0.0825x

It tries to continue.

Regards.
 
Re: ALGEBRA Profit problem.

that's what i do above.

i added $75+0.0825y=3997.75$ then $y=47548.48485$

what's wrong with my solution?
 
Re: ALGEBRA Profit problem.

bergausstein said:
that's what i do above.

i added $75+0.0825y=3997.75$ then $y=47548.48485$

what's wrong with my solution?

Hello.

A small firm, at the end of one year, the firm repays a total of $3997.75. (The amount + interests)

Repays: 1000.00+75.00+x+0.0825x=3997.75

For all these questions, you thinks that it is your money, and you will see like you are not wrong. :) If you give 1000.00 $ to one year, to an interest rate. You are satisfied if only they give you the interests?

It tries to continue. :)

Regards.
 
Re: ALGEBRA Profit problem.

the additional money lent is \$2700

the total money lent is \$3700.

simple interest rate of total loan is

$0.0825(y)+75=0.0825(2700)+75=297.75$

the simple interest rate for the total loan is 8% am i correct?
 
Re: ALGEBRA Profit problem.

bergausstein said:
the additional money lent is \$2700

the total money lent is \$3700.

simple interest rate of total loan is

$0.0825(y)+75=0.0825(2700)+75=297.75$

the simple interest rate for the total loan is 8% am i correct?

Yes.

8.047%

Regards.
 
  • #10
Re: ALGEBRA Profit problem.

mente oscura said:
...
It tries to continue...

Have you ever seen the movie The Silence of The Lambs? (Smile)

Your wording there puts me in mind of a character in the movie.
 
  • #11
Re: ALGEBRA Profit problem.

MarkFL said:
Have you ever seen the movie The Silence of The Lambs? (Smile)

Your wording there puts me in mind of a character in the movie.

(Rofl)

What?

Yes.

Yes, I have seen the movie. Whom do I him resemble?(Bigsmile)

Regards.
 
  • #12
Re: ALGEBRA Profit problem.

mente oscura said:
(Rofl)

What?

Yes.

Yes, I have seen the movie. Whom do I him resemble?(Bigsmile)

Regards.

Do you recall the serial killer "Buffalo Bill" that was keeping the young woman in a pit in his basement, and he would say things like:

"It rubs the lotion on its skin..."

"It puts the lotion in the basket..."

When you stated, "It tries to continue," I thought of this character. :D

I do apologize to the OP for hijacking the thread, but I just couldn't resist interjecting a bit of humor here and the thread seemed to have run its course.
 
  • #13
bergausstein said:
A small firm borrows \$1000 from a stockholder at a sim-pleinterest rate of 7.5%. The company secretary lends the firm an additional sum at a simple interest rate of
8.25%. At the end of one year, the firm repays a total of
\$3997.75. How much did the secretary lend the firm and
what is the simple interest rate on the total loan?

let

$y=$ additional money lent

$1000+y =$ total amount of money lent.

$1000(0.075)+0.0825y=3997.75$
This is incorrect. The left side is the interest accrued over the year. The right side is the total principle and interest. They are NOT equal.

$0.0825y=3997.75-75$

$y=47,548.48$ - additional money lent.

$1000+47,548.84 = 48548.48$ total amount of money lent.

$\frac{3997.75}{48548.48}=0.823=8.23\%$ interest rate on the total loan.i just want to confirm if my solution is correct. thanks!
 

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