Compound Interest: Quarterly/Monthly Cases Compound interest is a special interest rate calculation that considers interest earned not only on the princi...
Compound interest is a special interest rate calculation that considers interest earned not only on the principal amount but also on the accumulated interest from previous periods. This leads to a higher overall return compared to simple interest.
Quarterly and monthly cases are two common scenarios where compound interest is used.
Quarterly case:
Interest is calculated and added to the principal amount before calculating the next interest period.
This process is repeated quarterly, resulting in interest being added to the principal amount for a longer period of time.
Monthly case:
Interest is calculated and added to the principal amount after the end of each month.
This means that the interest is added to the principal amount before calculating the next interest period.
Example:
Suppose you invested $1000 for 6 months at an annual interest rate of 2%.
Quarterly case:
Month 1: Interest = 20.
Months 2, 3, 4, 5, 6: Interest = $1020 (add the quarterly interest to the principal amount).
Final principal = 20 = $1040.
Monthly case:
Month 1: Interest = 20.
Month 2: Interest = 20.40.
Month 3: Interest = 20.80.
Month 4: Interest = 21.20.
Month 5: Interest = 21.60.
Final principal = 20. = $1100.
As you can see, the quarterly case yields a higher total return due to the longer period of time the principal is invested.
Key Differences:
Frequency of interest calculation: Quarterly interest is calculated and added to the principal amount before the next interest period, while monthly interest is calculated and added after the end of each month.
Time period of compounding: Quarterly interest is calculated and added for a longer period of time, resulting in higher returns.
Compounding effect: Both cases allow the compound interest to accumulate over time, resulting in higher overall returns compared to simple interest