Table of Contents
What is Compound Interest?
Compound interest is the interest on the debt or deposit, i.e. the principal balance, plus the interest earned on the previous period. It multiplies the sum by the interest rate and continues to rise, often considered to be one of the most efficient investment methods.
Most banks use this method where they apply compound interest on savings, a benefit to account holders. If you are a user of a credit card, knowledge of the workings of compound interest calculations can be a motivation to pay off your balances quickly. Credit card companies charge interest on the principal balance and unpaid interest.
How to calculate Compound Interest?
Compound interest can be computed by multiplying the existing principal sum by one plus the annual interest rate raised by the number of compound periods minus one. The cumulative initial amount of the loan is subtracted from the resulting value. The formula to calculate compounding interest is as follows:
PV( 1 + r )^n = FV
PV = Present value
R = Rate of interest
N = Number of times interest is compounded
And FV = Future value
Here are a few examples that will be helpful in further understanding this concept.
Mr. A deposited $1000 in his savings account, with a rate of interest at 2% per month. He withdraws his amount at the end of every year. What will be his future value using compound interest?
Using the formula, his total amount will be $1268. It is becoming clear that Mr. A’s investment is growing, which demonstrates that the use of compound interest is deemed profitable.
Ali lent $10,000 to his business partner on a rate of return of 8% per annum. He will be paid back in 5 years with the total amount. What is the future value or the full amount Ali will get after five years?
Considering this formula, Ali will earn $14693, a profit of $4693.
Another example of compound interest, this time calculating present value having future value insight. Let us suppose Bright Co. wants to earn a profit of $100,000 after ten years at an 8% interest rate. How much does Bright Co. need to invest now to earn $100,000?
Now the FV will be divided by the interest rate, giving the amount
that needs to be invested now and assembling the formula such as this.
PV = FV / ( 1 + r )^n
PV = $100,000 / (1 + 8% ) ^10
PV = $46319.34
This illustrates the backward effect of the measurement of compound interest to derive the present value.
HOW COMPOUND INTEREST GROWS OVER TIME?
Compound interest works best when capital is left unused, which ensures that the longer you leave the investment, the more it grows. For example, if you invest $1,000 a year at 5% interest (compounded annually) for three years, you would have made $3472,875 and received $472,875 in interest.
It tends to multiply and increase over time, making it one of the best ways to use unused capital or to make new investments.
FREQUENCY OF COMPOUNDING
The level of compounding or how often interest is compounded is the same idea. In most cases, interest is compounded yearly but is often compounded monthly, quarterly, weekly, or regularly. However, in the compounding cycles, we learn more about this in-depth.
TIME VALUE OF MONEY
Time value of money (TVM) is the theory that money you have now is worth more than a similar amount in the future because of its possible earning power. The core concept of financing is that the money given will gain interest, every sum of money is worth more the faster it is earned. TVM is often referred to as the current discounted value.
In reality, only a few compounding methods are used which are
The interest is measured and paid on an annual basis. For example, Karim invested $1000 at a 5% interest rate for three years. Using formula FV = PV (1+r)^n, where n is 3, Karim earned $1157.625 after three years.
The interest is measured and paid after every three or four months. Let’s suppose, Karim invested $1000 at an annual interest rate of 10% compounded quarterly. What will be the total balance of Karim after three years?
Here the formula will change too,
FV = PV (1+r/n)^nt
Where t = number of years the amount is invested for
Karim will have $1344.88 after three years, compounding quarterly.
The interest is measured and charged every month, but this method is rarely practiced. Taking the example given above, Karim invested $1000 at an annual interest rate of 12% compounded monthly. What is the Future value after two years? Using the same formula of quarterly compounding, the total balance of Karim is $1269.73 compounded monthly.
By constant compounding, any interest obtained immediately
begins to gain benefit on its own. The secret to why Albert Einstein reportedly called compounding interest “The greatest mathematical achievement of all time”. This is true partly because unlike trigonometry or calculus taught in academia, compounding can be conveniently applied to everyday life.