# "Getting a personal loan from a bank" real life math problem - need a formula

• MHB
• GSJ1
In summary, you are borrowing money from a bank, and will have to make minimum monthly payments of 1% of the loan balance PLUS interest. The interest rate is 4.9% per annum calculated on a monthly basis (ie. 4.9%/12 each month) on the outstanding loan balance at the end of every month. At the end of the first month, you will have to pay 1% of the loan balance or $480, and at the end of the third year, you will have paid$47,520 in total.
GSJ1
Hi there,

Just wondering if anyone here can help me with a real life math problem I have on my hands right now!

I am going to borrow \$48,000 from a bank as an unsecured personal loan for a 3 year period. I have to make minimum monthly payments of 1% of the outstanding loan balance at the end of every month. And the interest rate is 4.9% per annum calculated on a monthly basis (ie. 4.9%/12 each month) on the outstanding loan balance at the end of every month. So at the end of the first month I will have to pay 1% X \$48,000 or \$480 as a minimum payment that month, and 4.9%/12 X \$48,000 = \$196 as interest. The loan balance then becomes \$48,000 - \$480 = \$47,520 at the end of the second month etc...

At the end of the 3 year period, what is the total amount of minimum monthly payments I will have made, assuming I pay down 1% of the outstanding loan balance each month.

At the end of the 3 year period, what is the total amount of interest payments I will have made, again assuming I pay down 1% of the outstanding loan balance each month.

Thanks so much.

If I have a number for this, then I can keep this money aside, and spend the rest of it, until I have to repay that amount in 3 years.

Hope that makes sense.

DISCLAIMER: Beer soaked rambling/opinion/observation/reckoning ahead. Read at your own risk. Not to be taken seriously. In no event shall the wandering math knight-errant Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.
GSJ1 said:
Hi there,

Just wondering if anyone here can help me with a real life math problem I have on my hands right now!

I am going to borrow \$48,000 from a bank as an unsecured personal loan for a 3 year period. I have to make minimum monthly payments of 1% of the outstanding loan balance at the end of every month. And the interest rate is 4.9% per annum calculated on a monthly basis (ie. 4.9%/12 each month) on the outstanding loan balance at the end of every month. So at the end of the first month I will have to pay 1% X \$48,000 or \$480 as a minimum payment that month, and 4.9%/12 X \$48,000 = \$196 as interest. The loan balance then becomes \$48,000 - \$480 = \$47,520 at the end of the second month etc...

At the end of the 3 year period, what is the total amount of minimum monthly payments I will have made, assuming I pay down 1% of the outstanding loan balance each month.

At the end of the 3 year period, what is the total amount of interest payments I will have made, again assuming I pay down 1% of the outstanding loan balance each month.

Thanks so much.

If I have a number for this, then I can keep this money aside, and spend the rest of it, until I have to repay that amount in 3 years.

Hope that makes sense.
Real life math problem? Maybe. Practical? Debatable.
Going by your minimum principal payment plan (and using Excel), I'd say it would take you 1,058 months, or 88.16 years to repay such a loan.
The last 114 months would entail interest payments of a mere 0.01 if this payment plan is followed to the letter.
On the other hand, the last 27 months would also entail principal payments a mere 0.01 under the same scheme.

Code:
month        payment            interest       balance
0                                           48,000.00
1    480.00+196.00=676.00      196.00       47,520.00
2    475.20+194.04=669.24      194.04       47,044.80
...
35    341.07+139.27=480.34      139.27       33,765.48
36    337.65+137.88=475.53      137.88       33,427.83
Your post is somewhat confusing; I think that you're saying
that the payment each month is 1% of the balance owing at
previous month-end PLUS the interest for the current month.

If that's correct, then the above "Bank statement format" shows
"what's going on", and that 33,427.83 will be the balance owing.

This can be easily verified: 48000 * .99^36 = 33427.83447...

The "1% payments" will total 14,572.17
The "interest payments" will total 5,950.30
So total payments = 14572.17 + 5950.30 = 20522.47

RECAP : 48000.00 - 20522.47 + 5950.30 = 33427.83

Can't think of a "cute formula" that'll spit out this full breakdown.
As Sir Jonah warns: you'll need something like Excel if you want
to set this up for other similar borrowing cases.

Total Payments paid at the end of 36 periods

Code:
48,000 - 48,000 (0.99^36)
48,000 - 33427.834466379539374768226179264
14572.165533620460625231773820736

14,572.17
Total Interest paid at the end of 36 periods

Code:
4.9%/12 * 48,000 * [(0.99^36 - 1)/(-0.01)]
4.9%/12 * 48,000 (30.358678195042626302566195459867)
4.9%/12 * 1457216.5533620460625231773820736
5950.3009262283547553029743101339

5,950.30

Wilmer said:
Code:
month        payment            interest       balance
0                                           48,000.00
1    480.00+196.00=676.00      196.00       47,520.00
2    475.20+194.04=669.24      194.04       47,044.80
...
35    341.07+139.27=480.34      139.27       33,765.48
36    337.65+137.88=475.53      137.88       33,427.83
Can't think of a "cute formula" that'll spit out this full breakdown.
As Sir Jonah warns: you'll need something like Excel if you want
to set this up for other similar borrowing cases.

Code:
month        payment            interest       balance
36    337.65+137.88=475.53      137.88       33,427.83

Code:
month
36

payment
48,000*(0.99^35-0.99^36) + 48,000*(0.99^35)*4.9%/12
=337.65+137.88=475.53

interest
48,000*(0.99^35)*4.9%/12
=137.88

balance
48,000 * 0.99^36
=33427.83

DISCLAIMER: Beer soaked rambling/opinion/observation/reckoning ahead. Read at your own risk. Not to be taken seriously. In no event shall the wandering math knight-errant Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.

I was waiting for some reaction from GSJ1 but you two just had to give away the entire solution.

jonah said:
I was waiting for some reaction from GSJ1 but you two just had to give away the entire solution.

Good things don't come to those who wait

I guess

DISCLAIMER: Beer soaked rambling/opinion/observation/reckoning ahead. Read at your own risk. Not to be taken seriously. In no event shall the wandering math knight-errant Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.
AbrahamA said:
Good things don't come to those who wait

I guess
And what good came upon thou who can't wait?

jonah said:
And what good came upon thou who can't wait?

A feeling of Highness just like the one from old days consuming Coke.

Last edited:
jonah said:
I was waiting for some reaction from GSJ1 but you two just had to give
away the entire solution.
Not to be taken seriously. In no event shall the wandering math
knight-errant Sir Wilmer aka Sir Denis in his caffeniated state be liable
to anyone for special, collateral, incidental, or consequential damages
in connection with or arising out of the use of his coffee
(and double cream, 1 sweetener) powered views.

Sincere apologies Sir Jonah.
I thought (from your earlier PM) that this is what you wanted:
somebody's version of the unclear problem.

I have already been sent to the corner by Sir Mean Mark, however
will stay a further half hour, and will wait for Sir Abe to join me.
Sir Abe, please bring pencil and paper, so we can play "X and O".

DISCLAIMER: Beer soaked rambling/opinion/observation/reckoning ahead. Read at your own risk. Not to be taken seriously. In no event shall the wandering math knight-errant Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.
AbrahamA said:
A feeling of Highness just like the one from old days consuming Coke.
Hallelujah! Praise Coke.

Wilmer said:

... (and double cream, 1 sweetener) powered views.
Careful about them sweeteners, Sir W.T. Caffeniated.
Heard them stuff are dangerous to one's mental health.
Especially that aspartame stuff.

Last edited:
jonah said:
I was waiting for some reaction from GSJ1 but you two just had to give away the entire solution.

We in fact do ask that people not "trample" on the help given by others by providing more hints or a full solution (MHB Rule #14), but we only ask that others wait for at least 24 hours before doing so. :D

MarkFL said:
We in fact do ask that people not "trample" on the help given by others by providing more hints or a full solution (MHB Rule #14), but we only ask that others wait for at least 24 hours before doing so. :D

@Mark

You mean, my forum account is kapoot for offering a complete solution that is akin to offering prohibited drugs to college freshmen

AbrahamA said:
@Mark

You mean, my forum account is kapoot for offering a complete solution that is akin to offering prohibited drugs to college freshmen

No, far more than 24 hours had elapsed, so all is good. :D

I am listing pros and cons of a personal loan vs such special loans. Hope that it is helpful.

lantranhana said:
I am listing pros and cons of a personal loan vs such special loans. Hope that it is helpful.
You are? WHERE is the "list"?

## 1. How do I calculate the interest on a personal loan?

The formula for calculating the interest on a personal loan is: Interest = (Principal Amount x Interest Rate x Time Period)/100. The principal amount is the total amount borrowed, the interest rate is the percentage charged by the bank, and the time period is the duration of the loan in years.

## 2. What is the minimum credit score required to get a personal loan from a bank?

The minimum credit score required to get a personal loan from a bank varies depending on the bank's policies and the type of loan. Generally, a credit score of 600 or above is considered good enough to qualify for a personal loan. However, a higher credit score may result in better interest rates and loan terms.

## 3. Can I use a personal loan for any purpose?

Yes, you can use a personal loan for any purpose such as debt consolidation, home improvements, medical expenses, or even to fund a vacation. However, it is important to remember that the loan amount and interest rates may vary depending on the purpose of the loan.

## 4. How much can I borrow through a personal loan?

The maximum amount you can borrow through a personal loan depends on various factors such as your credit score, income, and debt-to-income ratio. Generally, banks offer personal loans ranging from $1,000 to$50,000. It is important to only borrow what you need and can afford to pay back.

## 5. What is the process for getting a personal loan from a bank?

The process for getting a personal loan from a bank may vary slightly, but typically involves the following steps:

• Research and compare loan options from different banks
• Check your credit score and gather necessary documents
• Submit a loan application with the required information
• Wait for the bank to review and approve your application
• If approved, sign the loan agreement and receive the funds
• Make regular payments according to the loan terms

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