Confirm Interest Rate Solution on Total Loan

  • Context: MHB 
  • Thread starter Thread starter bergausstein
  • Start date Start date
  • Tags Tags
    Interest Rate
Click For Summary
SUMMARY

A small firm borrows $1000 from a stockholder at a simple interest rate of 7.5% and an additional amount from the company secretary at 8.25%. The total repayment after one year is $3997.75. The correct calculation shows that the secretary lent the firm $2700, resulting in a total loan amount of $3700. The simple interest rate on the total loan is 8.047%, confirming the calculations presented in the discussion.

PREREQUISITES
  • Understanding of simple interest calculations
  • Familiarity with algebraic equations
  • Knowledge of financial terms such as principal and interest rates
  • Ability to manipulate and solve equations
NEXT STEPS
  • Study the principles of simple interest and its applications in finance
  • Learn how to set up and solve algebraic equations involving multiple variables
  • Explore financial modeling techniques for loan calculations
  • Investigate the impact of varying interest rates on total loan repayment
USEFUL FOR

Finance students, loan officers, accountants, and anyone involved in calculating loan repayments and interest rates.

bergausstein
Messages
191
Reaction score
0
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!
 
Mathematics news on Phys.org
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!
 

Similar threads

MHB Optimizing Loan Interest Rates: Solving for Loan Length
  • · Replies 2 ·
Replies
2
Views
2K