# How to compare loans of same principal, same interest but with different tenors

I have a scenario where there are 2 loans that can be provided (assuming I am providing the loan). The principal amount is the same, 30,000 in case of both the loans. The interest is also same at 17%. The duration of one loan is 12 months and the other one is 24 months. The loans will be repaid with Equated Monthly Installments (EMI). The EMI for the 12 month loan is 2736 and the EMI for the 24 month loan is 1483.

In both cases, I have the option to re-invest the EMI at the same rate and same tenor. I want to understand which of the above loans will give me more returns and how to calculate the returns.

I have done a simple calculation but I am not convinced. For the 12 month loan I have taken the time in months for my principal to come back and then re-invest for another 12 months at the same rate. At the end of the 24 months, I gain 2*1 month EMI + Interest portion of EMI for 1 month. In this calculation, the 12 month loan re-invested is giving 5512 and the 24 month loan is giving 5598; which implies that the 24 month loan is more profitable. I am probably not taking in the condition that the EMIs could be re-invested on monthly basis.

Some help in understanding that and the actual process of calculation would be much appreciated.

• In the end are you asking how much money you will have after 24 months or 48 months? – mhoran_psprep Feb 9 '18 at 11:54
• I am asking how much money will I have after 24 months. – Ironluca Feb 9 '18 at 11:58

Let's cover some assumptions first. I slightly verified these by throwing the numbers into a spreadsheet and making sure that they made sense. But of course, I can't read your loan agreement.

1. The 17% is an annual rate. The monthly rate will be about 1.4167%.
2. You will be reinvesting at the same rate and from either loan on a monthly basis.

If those assumptions hold, then it doesn't matter. Your rate is the same in either loan. You put in 30,000 and get back the 30,000 plus interest. If you reinvest continually, your total principal will increase by about 1.4% a month. However, most of your money will be tied up in loans. You'll only be able to access a small amount of it. For the twelve month loan (reinvested in other twelve month loans), that looks to be 3819.68. For the twenty-four month, 2070.39.

In both cases, after twenty-four months, your principal grows to about 41,882.46. That's misleadingly precise. The exact amount will depend on exactly how they round and how long it takes to reinvest.

It would take you twelve to twenty-four months to extract all your money. And that's the major difference between the two. The longer loan takes longer to get your money out.

The major advantage of the longer loan is that the interest rate can't decrease for the life of the loan. Of course, if interest rates go up, that becomes a disadvantage. The other disadvantage is that it takes longer to get your money out.

It it's worth noting that in many countries, like the United States, a 17% rate is so good (for the lender) as to suggest a scam. Of course, that calculation changes in countries with higher rates of inflation. I couldn't say whether that is a good or bad rate in India for example. It looks high to me, even for India, but then I'm used to 17% being a bad credit card rate.

It's also unclear to me how much risk you face. Might the borrower or borrowers not repay the loan? If so, what happens? How likely is that? This might be a great deal now and then utterly collapse, losing all your money, in a recession.

With principal `s`, interest rate `r`, `n` months and repayments `d12` and `d24`.

``````s = 30000
r = 17/100/12

n   = 12
d12 = (r (1 + r)^n s)/(-1 + (1 + r)^n) = 2736.14

n   = 24
d24 = (r (1 + r)^n s)/(-1 + (1 + r)^n) = 1483.27
``````

Return on two 12 month loans (of 30,000)

``````2 (12*d12 - 30000) = 5667.42
``````

Return on one 24 month loan

``````24*d24 - 30000 = 5598.43
``````

So you gain `5667.42 - 5598.43 = 68.99` with the two 12 month loans.

If you re-invest all your returns from the first 12 month loan

``````s2 = 12 d12 = 32833.71
n  = 12
d  = (r (1 + r)^n s2)/(-1 + (1 + r)^n) = 2994.59

12 d - 30000 = 5935.08
``````

then you gain `5935.08 - 5598.43 = 336.65` with the two 12 month loans.