Interest is either your best friend or your worst enemy. It can work for you as an asset, or against you as a liability. But how does it work? In this post, we will discuss the basics of interest rates.
WHAT YOU NEED TO KNOW
A person borrowing money is a debtor. The person lending money is a lender. When a debtor takes a loan from the lender, the lender expects to be paid back. If the debtor cannot pay the loan back immediately, the lender will ask for interest. Interest is the percentage of a sum that is paid in return for delaying the full payment of a sum.
Interest is meant to protect the lender from inflation and risk. It is both an incentive for the lender to lend money, and a fee for the borrower as payment in return for the lender’s service.
The amount of interest applied to a sum is usually a percentage of the sum applied daily, monthly, or yearly. The rate is dependent on the amount borrowed, how long until the debtor can pay back the full amount of the loan, and how risky the lender considers the overall loan given the debtor. A person borrowing funds wants the least amount of interest applied. A person lending or investing money wants the most amount of interest applied
If you have liabilities, you are most likely paying interest to someone. If you have assets, you are most likely receiving interest from someone. Every loan is someone else’s investment. You ultimate goal should be to never pay interest, only receive it.
HOW DOES INTEREST WORK?
The best way to explain how interest works is through an example. Let’s say a student, Barry Borrow, needs to borrow $10,000 to finish funding his college education. He has three options:
- Take a loan from his parents. His parents offer to give him $10,000 at a 0% interest rate while Barry attends college.
- Take a loan from a lender, let’s call them CollegeNow, who is willing to lend Barry the $10,000 in exchange for an interest rate of 5% APY compounded daily. CollegeNow tells Barry that he does not need to make payments on the $10,000 while attending college. However, Barry does need to pay the interest accrued on the loan at the end of every year.
- Take a loan from a lender, let’s call them PayEmMore, who is also willing to lend Barry the $10,000 in exchange for an interest rate of 5% APY compounded daily. PayEmMore tells Barry he does not need to pay anything towards the loan while he is attending college.
Let’s see how much Barry owes at the end of each year and upon graduation.
Depending on which loan Barry chooses, at graduation he would have:
- Paid nothing to his parents, but owe them a total of $10,000.
- Accumulated and paid $2,046.39 to CollegeNow, and owe them a total of $10,000.
- Paid nothing to PayEmMore, and owe them a total of $12,213.86.
So, why would the PayEmMore loan cost Barry an additional $167.47 for a loan with the same term and same rate? It is because compounding acted on the accumulated interest.
HOW DOES COMPOUNDING WORK?
Interest is calculated using a formula with three variables: principle, rate, and time. Principle is the amount of money to which the interest rate is being applied. The rate is the interest, or percentage of the sum, to be applied each loan term. The time is usually the length of the term.
Interest = Principle x Rate x Time
I = Prt
Let’s say you had $10,000 at a rate of 5% compounded yearly. You could calculate the yearly interest by using the formula. The $10,000 is the principle. The 5% is the rate, which is expressed as the decimal point equivalent of 0.05 in this formula. To figure out the interest after one year, the time would be entered as one year.
I = $10,000 x 0.05 x 1 = $500
Now let’s say the compounding occurs monthly, rather than yearly. This changes the calculation a bit. Rather than the interest being applied once during the year, it is applied to the principle every month. The principle for the first month is still $10,000. The rate is now 5% divided by 12 months, so 0.42% or 0.0042 as a decimal point. We need to calculate the interest for the first compounding term, which is 1 month.
First Month’s Interest = $10,000 x 0.0042 x 1 = $41.67
Now, you can only calculate the second month by accounting for the first month’s interest in the equation.
Second Month’s Interest = ($10,000+$41.67) x 0.0042 x 1 = $42.18
You continue this process for all twelve months until you get to the final month.
$511.62 is greater than $500, so you can infer from this exercise that the more frequent the compounding, the greater the amount of interest you will accumulate.
Sometimes compounding occurs more often than monthly, such as daily. It would be cumbersome to calculate the interest for each compounding term, so there is another formula we can use.
Interest = Principle x (1+Rate/Number of Compounding Periods)^(Number of Compounding Periods x Time)
I = P(1+r/n)^(nt)
Using the monthly compounding example, we could calculate the interest at the end of the year using one formula. The principle is $10,000 at the beginning of the 1 year term. The interest is still 5%, .05 as a decimal. And we are compounding monthly, so the number of compounding periods is 12 over a 1 year term.
$10,000 x (1+0.05/12)^(12 x 1) = $10,511.62
Using this formula is especially convenient for large periods, such as daily compounding.
$10,000 x (1+0.05/365)^(365 x 1) = $10,512.68
Note, the interest for daily compounding is more than the monthly compounding option, further proving that increased compounding periods result in a greater accumulation of interest. However, there is a limit to the effectiveness of increasing periods for increased interest production.
Let’s try compounding continuously, let’s say 1,000 compounding periods in one year (or nearly 3 times as much as daily compounding).
$10,000 x (1+0.05/1,000)^(1,000 x 1) = $10,512.70
Note, the amount of interest increased 2.32% by compounding once a month instead of once a year. The amount of interest only increased by 0.21% from monthly to daily compounding. Daily to continuous compounding made a negligible difference to the accumulated interest.
HOW RATES AFFECT COMPOUNDING
We have been focusing on one interest rate so far, but what would happen if the rate increased or decreased. Let’s say someone, Molly Money, had several options for an investment opportunity. She had $10,000 to invest for five years. What would be Molly’s total portfolio at the end of each year given several interest rate options compounded yearly.
We can observe from the chart that the greater the rate, the faster compounding increases the principle. Therefore, Molly Money should prefer an investment with as large a rate as possible when investing.
Your main goal should be to have no interest working against you. If you have loans, pay them off as quickly as possible. Avoid spending or borrowing money you do not have. If you have to get a loan, get as low a rate and as infrequent a compounding period as possible.
The ultimate goal is to invest in ventures that earn you interest. Earning passive income is possible with wise investing. Passive income allows you to earn money with very little effort, essentially in your sleep. With enough investments, you can earn enough to live off of the interest you earn instead of earning income from traditional work. If you are seeking to invest, go for as high a rate and as frequent a compounding period as possible.
Has this post inspired you to earn interest rather than pay it? Let me know in the comments below!
Next time, we will discuss inflation.