Need help finding an interest rate on a loan

[Scmiller430]

Hi there I need some help figuring out an interest rate for a loan contract that will be compounded monthly

The principal amount is $81,000
The first 12 months there will be a $1000 payment received each month
The next twelve months there will be a $2000 payment received each month
At the end of 24 months from the initial time of borrow, the remaining balance will be paid in full.
The total amount paid will be $85,000 meaning there will be $4000 in interest paid. What is the interest rate if the balance is compounded monthly?

Thanks so much for your help!

 

[Deleted member 4993]

Hi there I need some help figuring out an interest rate for a loan contract that will be compounded monthly

The principal amount is $81,000
The first 12 months there will be a $1000 payment received each month
The next twelve months there will be a $2000 payment received each month
At the end of 24 months from the initial time of borrow, the remaining balance will be paid in full.
The total amount paid will be $85,000 meaning there will be $4000 in interest paid. What is the interest rate if the balance is compounded monthly?

Thanks so much for your help!

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Steven G]

Hi there I need some help figuring out an interest rate for a loan contract that will be compounded monthly

The principal amount is $81,000
The first 12 months there will be a $1000 payment received each month
The next twelve months there will be a $2000 payment received each month
At the end of 24 months from the initial time of borrow, the remaining balance will be paid in full.
The total amount paid will be $85,000 meaning there will be $4000 in interest paid. What is the interest rate if the balance is compounded monthly?

Thanks so much for your help!

Your definition of help is not the same as the way help is used in our posting guidelines.

 

[Scmiller430]

Your definition of help is not the same as the way help is used in our posting guidelines.

My apologies I’m unsure of how to ask my question in the correct way then. I’m having trouble figuring out what the interest rate would be and I’ve tried a few different ways but I can’t seem to come up with the correct solution

 

[Scmiller430]

My apologies I’m unsure of how to ask my question in the correct way then. I’m having trouble figuring out what the interest rate would be and I’ve tried a few different ways but I can’t seem to come up with the correct solution

I would like to learn how to do a problem like this if it were to come up again in the future for me

 

[Otis]

I’m unsure of how to ask my question

Hi Scmiller. Did you happen to look at the forum guidelines at the links you were provided? They pretty much explain how to ask for help in the forum. They also advise that, unless you say otherwise, we'll treat you like a student who is stuck on a homework exercise. We don't complete homework, but we'll tutor, and for that we need people to share where they're at in the exercise.

if it were to come up again in the future for me

Hmm, that seems to suggest that you might not be a student taking a math class. What's your situation?

Do you have experience working with loans?

Can you use technology (eg: graphing calculator, spreadsheet, math software, coding in your favorite language)?

Have you ever completed an ammortization schedule (with regular payments) by hand, when you do know the interest rate?

I'm not one of the financial-math people here (that is, there may exist shortcut formulas for paper-and-pencil methods that I don't know), but I do know how to automate guess-and-check steps that will "zero in" on the rate generating exactly $4000 interest with those irregular payments. I don't know whether such an approach would be appropriate or helpful for you because I don't know what you already understand about loans or what resources are available to you. I'll wait for your response.

?

 

[Deleted member 4993]

Hi there I need some help figuring out an interest rate for a loan contract that will be compounded monthly

The principal amount is $81,000
The first 12 months there will be a $1000 payment received each month
The next twelve months there will be a $2000 payment received each month
At the end of 24 months from the initial time of borrow, the remaining balance will be paid in full.
The total amount paid will be $85,000 meaning there will be $4000 in interest paid. What is the interest rate if the balance is compounded monthly?

Thanks so much for your help!

There were some money paid in lump-sum at the end of 24 months to bring the total pay-back to 85 K.

How much total money was paid back (in installment s) at the end of 12 months?

How much total money was paid back (in installment) in next 12 months?

How much total money was paid in lump-sum?

 

[Otis]

For any readers who are interested, here's what I did (coding a 24-month loop to guess-and-check interest rates).

The current loan balance (cBAL) starts at 81000

The monthly payment (mPMT) starts at 1000 and doubles after the twelfth payment

The annual interest rate is R, so the monthly interest rate is R/12

At the end of each month, part of the payment is for that month's interest (iPMT) and the remainder is applied to the loan balance (bPMT)

The interest part of each payment is:
iPMT = R/12 * cBAL (rounded to the nearest cent)

The loan balance part of each payment is:
bPMT = mPMT - iPMT

iTOT is for keeping a running total of the interest paid

PSEUDOCODE
----------

R = <my guess>
cBAL = 81000.
mPMT = 1000.
iTOT = 0

for n from 1 to 24
  iPMT = round(R/12*cBAL, 2)
  bPMT = mPMT - iPMT
  cBAL = cBAL - bPMT
  iTOT = iTOT + iPMT
  print(n, iPMT, bPMT, cBAL)
  if n = 12 then
    mPMT = 2000.
  endif
next n

print(iTOT)

1st guess R = 0.03 \ result iTOT = 4133.13
2nd guess R = 0.025 \ result iTOT = 3778.74
3rd guess R = 0.029 \ result iTOT = 3991.16
7th guess R = 0.02906 \ result iTOT = 3999.66
10th guess R = 0.0290624 \ result iTOT = 4000.00

?

 

[jonah2.0]

Near death contribution follows.

Hi there I need some help figuring out an interest rate for a loan contract that will be compounded monthly

The principal amount is $81,000
The first 12 months there will be a $1000 payment received each month
The next twelve months there will be a $2000 payment received each month
At the end of 24 months from the initial time of borrow, the remaining balance will be paid in full.
The total amount paid will be $85,000 meaning there will be $4000 in interest paid. What is the interest rate if the balance is compounded monthly?

Thanks so much for your help!

[imath]81000\left(1+\frac{j}{12}\right)^{24}-1000\frac{\left(1+\frac{j}{12}\right)^{12}-1 }{\frac{j}{12}}\left(1+\frac{j}{12}\right)^{12}-2000\frac{\left(1+\frac{j}{12}\right)^{12}-1 }{\frac{j}{12}}=85000-12*1000-12*2000[/imath]

solve 81000(1+j/12)^24-1000((1+j/12)^12-1)/(j/12)*(1+j/12)^12-2000((1+j/12)^12-1)/(j/12)=85000-12000-24000 - Wolfram|Alpha

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Have a nice day friends and math knight-errants.