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

[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.

 

[jonah1]

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.

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.

One way of answering your questions is by use of spreadsheet programs.
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.
If you want your questions answered, one word: Spreadsheet.

 

[Wilmer]

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.

 

[AbrahamA]

Total Payments paid at the end of 36 periods

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

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

 

[AbrahamA]

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.

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

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

 

[jonah1]

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.

 

[AbrahamA]

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

 

[jonah1]

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.

Good things don't come to those who wait

I guess

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

 

[AbrahamA]

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

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

 

[Wilmer]

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

DISCLAIMER: Coffee 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 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".

 

[jonah1]

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.

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

Hallelujah! Praise Coke.

 

[jonah1]

... (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.

 

[MarkFL]

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

 

[AbrahamA]

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

 

[MarkFL]

@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

 

[lantranhana]

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

 

[Wilmer]

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"?