Compound Interest is the interest paid on both the principal and the interest you earned so far on that principal.
Suppose you invested $500 for 4 years in a bank and the bank pays 2% compound interest annually.
By the end of the first year, your account balance would be
$500 + 2% of $500 = $500 + $10 = $510.
For the second year, this $510 will be considered as the principal and the interest will be worked out for this amount.
That means, the interest for the second year will be calculated on the principal $500 and the interest $15.
The same process will continue for 4 years.
A. $1,092.73
B. $1,047.89
C. $1,085.69
D. $1,023.58
Correct Answer: A
Step 1: The balance in the account is equal to the sum of the principal and the simple interest.
Step 2: The rate of interest is 3% i.e. 0.03.
Step 3: To calculate the compound interest for three years, make a spreadsheet as shown below.
| Principal at the beginning of each year |
Interest |
Balance |
|
Year 1: $1,000.00 |
1,000.00 × 0.03 = 30 |
1,000.00 + 30 = 1,030.00 |
|
Year 2: $1,030.00 |
1,030 × 0.03 = 30.90 |
1,030.00 + 30.9 = |
|
Year 3: $1,060.90 |
1,060.90 × 0.03 = 31.83 |
1,060.90 + 31.827 = 1,092.73 |
Step 4: So, the balance at the end of 3 years is $1,092.73.
Q1: If $1000 is invested at 5% compound interest annually, what is the balance after 2 years?
Q2: Which of the following will result in the highest return?
Q: What is the difference between compound and simple interest?
A: Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus accumulated interest.
Q: How does the compounding frequency affect the interest earned?
A: The more frequently interest is compounded (e.g., daily vs. annually), the higher the total interest earned will be over time.