# How to know how much interest paid per payment in a fixed tenor personal loan

I recently took up a personal loan. I do not have any financial background and I do not have any issue paying the loan but I am just curious on how they come out with some numbers.

To be precise, the loan in question is Standard Chartered CashOne Loan which you can follow the link for more details. To be honest it's not the best loan in town but I wasn't that wise at that time when choosing up a loan package. My bad.

Anyway, here are the numbers I have in the agreement letter I received last year:

``````Loan Amount: \$9,800
Loan Period: 36 months
Actual Applied Rate: 7.5% per annum
Effective Interest Rate: 13.69% per annum
One time processing fee: \$199 (So they actually reimbursed me \$9,601)
Monthly instalment: \$333.47
``````

So follow these facts, I can deduce the following numbers:

``````Total Interest = \$9,800 * 0.075 * 3 = \$2,205
Hence, Total Payable = \$9,800 + \$2,205 = \$12,005
``````

So if I divide \$12,005 by 36 months, I get \$333.47 monthly payable.

So now, what I don't understand is, how do they calculate how much money is paid to the interest, and how much money is paid to the principal when I dump the \$333.47 to the bank every month? What's the formula to this thing?

To illustrate this, look at the table below:

``````Month #       Loan Balance        Interest       Principal      Repayment
-------------------------------------------------------------------------
1             \$9,800.00           \$111.81        \$221.66        \$333.47
2             \$9,578.34           \$109.28        \$224.19        \$333.47
3             \$9,354.15           \$106.72        \$226.75        \$333.47
4             \$9,127.40           \$104.14        \$229.34        \$333.47
5             \$8,898.06           \$101.52        \$231.95        \$333.47
6             \$8,666.11            \$98.87        \$234.60        \$333.47
.......
.......
34              \$978.02            \$11.16        \$322.31        \$333.47
35              \$655.71             \$7.48        \$325.99        \$333.47
36              \$329.71             \$3.76        \$329.71        \$333.47
-------------------------------------------------------------------------
Total                           \$2,205.00      \$9,800.00     \$12,005.00
``````

Following the advertised table on their CashOne website, I noticed the interest column is calculated based on the `remaining loan balance x a number`. This number is fixed throughout the 36 months, and hence I roughly (stupidly using excel) hand calculated it to be 0.01140924.

For example, for month #2, `\$9,578.34 * 0.01140924 = \$109.28` and vice versa.

Question is, what is this number `0.01140924` and how do I get it from a formula? I believe it's a simple mathematical equation.

In addition, how does one come out with the EIR as `13.69% pa`? How do you obtain it via a formula? Is this something the bank decided or is it calculated based on the loan amount and tenor I chose?

I googled that `EIR = (1 + i/n)^n - 1` but it doesn't seem to apply here? What am I missing here? I believe it's just some simple calculation but I can't seem to reach it.

Thanks!

## Edit

If you are interested, here is the link to the excel sheet I managed to come out with, with all the calculations there. You can copy it for your own if you need to.

Question is, what is this number 0.01140924

13.69/12=0.01140924

In addition, how does one come out with the EIR as 13.69% pa?

When calculating payments, PV = 9800, N=36 (months), PMT=333.47, results in a rate of 1.140924% per period, and rate of 13.69%/yr.

No idea how they claim 7.5%

In Excel, type

=RATE(36,333.47,-9800,0,0)

And you will get 1.141% as the result.

36 = #payments, 333.47 = payment per period, -9800 is the principal (negative, remember this) And the zeros are to say the payments are month end, second zero is the guess.

Edit - I saw the loan is from a Singapore bank. It appears they have different rules on the rates they quote. As quid's answer showed the math, here's the bank's offer page - The EIR is the rate that we, not just US, but most board members, are used to. I thought I'd offer an example using a 30 year mortgage. Yo can see above, a 6% fixed rate somehow morphs into a 3.86% AR. No offense to the Singapore bankers, but I see little value in this number. What surprises me most, is that I've not seen this before.

What's baffling is when I change a 15yr term the AP drops to less than half. It's still a 6% loan and there's nothing about it that's 2 percent-ish, in my opinion.

Now we know.

• So now I know that 13.69 is derived from 0.01140924 * 12 (EIR in a year). How do you calculated out 1.140924% anyway? Thanks anyway! – Lionel Chan Feb 22 '16 at 11:09
• You use a finance calculator, or the finance equations within Excel or other spreadsheet software. – JTP - Apologise to Monica Feb 22 '16 at 11:37
• @LionelChan Chances are it has been rounded off, as you aren't using the final/original numbers. You are back calculating. – DumbCoder Feb 22 '16 at 12:58
• I don't have financial background so may I know how 13.69 and 1.14% is being derived? Or, what term should I googling to learn more? It pissed me off because 1. I don't know what I am dealing with and 2. Why the number is so. Thanks! – Lionel Chan Feb 22 '16 at 14:43
• When your numbers are plugged in, the amount borrowed, the number of payments, and the payment amount, the one thing missing is the interest rate and that is what a spreadsheet or calculator will solve for. – JTP - Apologise to Monica Feb 22 '16 at 14:55

The "Actual Applied Rate" of 7.5% is the total amount of interest charged over the life of the loan, \$2,204.82, divided by the loan amount divided by three years.

``````\$2,204 / \$9,800 = 22.5%

22.5% / 3 Years = 7.5%
``````

This amount is lower than the actual interest rate of 13.69% because interest charges are based on loan principle which reduces over the life of the loan.

• +1 but, huh? I appreciate the math, but that number is not a legit apr, I've never seen that calculation, which basically obfuscates the high cost of this loan. In my opinion, there's nothing 7%ish about this loan. Bad lender. – JTP - Apologise to Monica Feb 22 '16 at 18:43
• I agree. It's a nonsense so the sales people can cite a number lower than the real interest rate. But since I'd never heard of "Actual Applied Rate" I cranked up Excel to find something that came to 7.5, and this was it. – quid Feb 22 '16 at 18:47
• Yea I'm still pissed off by my wrong decision. Anyway I thought 7.5% is given, and 13.69% is derived? Check their packages page sc.com/sg/borrow/personal-loans-cashone.html – Lionel Chan Feb 22 '16 at 22:49
• @LionelChan 7.5% is the derived number, because it's only available after calculating the total interest paid on a 36 month 13.69% loan. – quid Feb 23 '16 at 2:35

The 1.140924% is calculated by taking 13.69%/12 = 1.140924%. Dividing this number by 100 gives you the answer 1.140924 / 100 = .01140924. When dealing with decimals it's important to remember the relationship between a decimal and a percent. 1% = .01

To return .01 to a percent you must multiple that number by 100. So .01 x 100 = 1%

In order to get a decimal from a percent, which is what is used in calculations, you must divide by 100.

So, here if we are trying to calculate how much interest you are paying each month we can do this:

9800 * .1369 = \$1341.62 (interest you will pay that year IF the principal balance never changed) 1341.62 / 12 = ~111.81

Now, month two 9578.34 * .1369 = 1311.274746 1311.274746 / 12 = 109.28

In order to get your monthly payments (which won't change) for the life of the loan, you can use this formula:

Monthly payment = r(PV) / (1-(1+r)^-n)

Where: r= Interest Rate (remember if calculating monthly to do .1369/12) PV= Present Value of loan n=time of loan ( in your case 36 since we are talking monthly and 12*3 = 36)

from here we get: [(.1369/12)*9800]/(1-(1+.1369/12)^-36) = \$333.467 when rounding is \$333.47

As far as actual applied interest rate, I'm not even sure what that number is, but I would like to know once you figure out, since the interest rate you're being charged is most definitely 13.69%.

• Appreciate that! So meaning the EIR 13.69% is a number given by the bank, not by any form of calculation from the 7.5%? Because I don't see any derivation of this number at all. – Lionel Chan Feb 22 '16 at 22:44
• 13.69xxxx% is your APR. – DukeLuke Feb 23 '16 at 13:53
• Thanks. I finally understand what's that about. Sucker lender – Lionel Chan Feb 24 '16 at 0:28