Compound interest is earning interest on interest already earned. A savings account earns interest on the initial deposit and credits to the account balance. Now the account balance is the initial deposit and the interest earned. The next interest payment is calculated on the account balance which includes the interest earned before.
The account is earning interest on interest.
Simple Interest on Savings
Simple interest means that interest is paid on your account balance at the end of the investment period.
To calculate simple interest multiply the principal by the rate of interest by the term of the loan. The principal is the amount of money borrowed or invested. The rate of interest is the percentage applied to the principal for its loan or investment. The term of the loan or investment is the number of periods the principal earns or pays interest.
The period can be days, months or years.
Example
A bank pays 6% per annum on 1 year term deposits. How much interest will a deposit of $50,000 earn in one year.
$50,000 x 0.06 = $3,000 per year
Example
A bank pays 6% per annum on 1 year term deposits. How much interest will a deposit of $500,000 earn each month.
$500,000 x 0.06 / 12 months = $2,500 per month
Compound Interest on Savings
Compound interest means the simple interest earned on the savings are reinvested to earn more interest.
Simple interest is calculated on the original principal amount. The amount of interest earned each period is constant. When calculating compound interest, the principal is increased by reinvesting the interest earned at the end of each period.
The power of compounding exponentially earns money in an account. The longer you save and invest money, the more interest you earn. Eventually, you earn more interest on a larger account balance that resulted from years of earning interest on previous interest earnings.
The key to earning more money is to start saving early, reinvest the interest and save regularly.
Example
A bank pays 6% per annum on 1 year term deposits. How much interest will a deposit of $50,000 earn in three years with compounding interest?
1st Year: $50,000 x 0.06 = $3,000 interest
2nd Year: $53,000 x 0.06 = $3,180 interest
3rd Year: $56,180 x 0.06 = $3,370 interest
At end of year 3: Balance = $59,550
Simple interest earned $3,000 per year, so 3 years simple interest is $9,000.
Compound interest earns more interest each year giving total interest $9,550.
Reinvesting the interest earned an extra $550 over the 3-year period.
Compound Interest Formula
The higher the interest rate for an account and the more frequent the compounding, the more interest you will earn over time.
To calculate compound interest, use the formula:
S = P x (1 + i)n
S = Accumulated Sum
P = Principal (starting balance)
i = interest rate per compounding period as a decimal (for example, 5% becomes 0.05)
n = number of compounding periods
Example
A person places $50,000 cash in a deposit account that pays interest rate of 6% per year, compounded monthly. How much interest is earned in two years?
Divide the annual interest rate of 6% by 12 (as interest compounds monthly)
i = 0.06 / 12 = 0.005
Calculate the number of time periods (n) in months you’ll be earning interest for:
n = 2 years x 12 months per year = 24 periods
Use the compound interest formula
S = $50,000 x (1+ 0.005)24
= $50,000 x 1.1272
= $56,360
Example
A person places $50,000 cash in a deposit account that pays interest rate of 6% per year, compounded annually. How much interest does the deposit earn in two years?
Divide the annual interest rate of 6% by 1 (as interest compounds yearly)
i = 0.06 / 1 = 0.06
Calculate the number of time periods (n) in yearsyou’ll be earning interest for:
n = 2 years
Use the compound interest formula
S = $50,000 x (1+ 0.06)2
= $50,000 x 1.1236
= $56,180
Note: An account that pays interest compounding monthly will earn more interest.
Perpetuity
A perpetuity is when a series of future cash flows continues forever.
The present value of a perpetuity is A = R / i
A = Amount that needs to be invested
R = Return to be earned
i = annual interest rate
Example
An investor wishes to earn $20,000 per year from a bank term deposit. How much principal needs to be invested at 5% interest per year to earn $20,000 every year forever?
A = $20,000 / 0.05 = $400,000
Note: In this case, there is no compounding interest.
Compound Interest on Loans
Compounding interest on a loan means the interest owed is added to the balance of the loan. If you don’t pay the interest payment the loan account is charging interest on interest.
The more loan repayments you fail to pay, the more interest you will owe.
Example
A bank loan of $50,000 charges 10% interest per annum on a 3-year loan. How much interest will accumulate in three years with no loan payments?
1st Year: $50,000 x 0.10 = $5,000 interest
2nd Year: $55,000 x 0.10 = $5,500 interest
3rd Year: $60,500 x 0.10 = $6,050 interest
At end of year 3: Loan Balance = $66,550
With no loan repayments, the bank compounds the interest and you end up with a larger loan balance.
Please read Why Home Loan Interest Rates Are Low
How to Take Advantage of Compound Interest
Savings & Investment
Start Saving As Soon As Possible
The power of compounding takes time to work. The longer you save money the more interest you earn and the more the compounding effect.
Save More Frequently
Add money to your savings & investments every month. Try to establish a savings account or term deposit with monthly interest payments. Reinvest the interest earnings every month to earn more interest income.
Invest More Money Every Year
If you regularly save a fixed amount every month, increase the amount invested every year. Now your savings are increasing faster and the compounding interest effect is working in your favor.
Invest Lump Sums
If you receive a lump sum of money invest it into your savings account.
Delay Making Purchases
Consider delaying a purchase for a few months and keep the money in your savings account to earn more interest income.
Ensure the Interest Rate is Competitive
Try to get the highest interest rate on your investment accounts to earn the most amount of interest. Check there are no hidden account fees.
Invest into an Account that Pays Interest More Frequently
Invest into an account that pays interest more frequently, such as monthly or quarterly rather than annually. Your account will earn more interest on interest.
Loans
Borrow Less Money
The less money you borrow the less interest you will pay.
Many homeowners end up paying more interest on their home loans than the increased value of their home.
Keep the loan as small as possible to avoid paying large amounts of interest to banks.
Make more frequent Loan Repayments
Interest calculated on loan balances are most often calculated daily and charged to the loan every month.
Making more frequent loan repayments reduces the amount of loan interest charged to the loan. Paying weekly instead of monthly will save thousands of dollars in interest and shorten the term of the loan.
For example, if you pay $2000 per month, instead pay $500 per week to reduce the loan interest.
Increase the Loan Repayment Every Year
If you are paying back a long-term loan like a home mortgage, increase the monthly repayment amount every year. The increased repayment reduces the interest payment and reduces the term of the loan.
For example, if you pay $2000 per month increase the repayment amount by $50 per month every year.
Ensure the Interest Rate is Competitive
Try to get the lowest interest rate on your loans to pay the least amount of interest. Check for other fees and charges such as early repayment fees.
Invest Lump Sums
If you receive a lump sum of money make an extra payment into your loan account to save interest.
Islamic Finance
Please read An Islamic Mortgage is Different from a Conventional Mortgage
