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Compound interest

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Krysten Amoranto

This document defines key terms related to compound interest such as compound interest, compound amount, compounding period, total number of conversion periods, and periodic rate. It provides the formulas for calculating compound interest, compound amount, periodic rate, and total number of conversion periods. Examples are given to show how to apply these concepts and formulas to calculate compound interest and compound amount for given principal amounts over various time periods and interest rates compounded at different frequencies.

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Compound interest
Compound Interest (I) an interest resulting from the periodic addition of simple interest to the principal amount. Formulas: I = F P and I = P [ (1 + i) n 1]
Compound Amount (F) an accumulated amount composed of the principal and the compound interest. Formula: F = P (1 + i) n
Compounding or Conversion period (m) number of times in a year the interest will be compounded.
annually ; m = 1 semi-annually; m = 2 quarterly; m = 4 monthly; m = 12 weekly; m = 52 daily; m = 360
Total Number of Conversion Period (n) product of time (number of years) and the conversion period. Formula: n = tm
Periodic Rate (i) quotient of rate and conversion period. Formula: i = r/m
Note: If the conversion period is not indicated in the problem, then it is assumed to be compounded annually, so m = 1.
Example 1: Find the compound amount and compound interest of P 4,000 for 4 years and 6 months compounded at 4% semi-annually.
Example 2: Robbie wanted to put his money of P 38,000 in a bank so that it will grow but he put it in a bank that will compound his money semi-annually at 7% by 3 years and 2 months. What is the compound interest?
Example 3: Accumulate P 16,000 in 16 months at 16% semi-annually.

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Compound interest

  • 2. Compound Interest (I) an interest resulting from the periodic addition of simple interest to the principal amount. Formulas: I = F P and I = P [ (1 + i) n 1]
  • 3. Compound Amount (F) an accumulated amount composed of the principal and the compound interest. Formula: F = P (1 + i) n
  • 4. Compounding or Conversion period (m) number of times in a year the interest will be compounded.
  • 5. annually ; m = 1 semi-annually; m = 2 quarterly; m = 4 monthly; m = 12 weekly; m = 52 daily; m = 360
  • 6. Total Number of Conversion Period (n) product of time (number of years) and the conversion period. Formula: n = tm
  • 7. Periodic Rate (i) quotient of rate and conversion period. Formula: i = r/m
  • 8. Note: If the conversion period is not indicated in the problem, then it is assumed to be compounded annually, so m = 1.
  • 9. Example 1: Find the compound amount and compound interest of P 4,000 for 4 years and 6 months compounded at 4% semi-annually.
  • 10. Example 2: Robbie wanted to put his money of P 38,000 in a bank so that it will grow but he put it in a bank that will compound his money semi-annually at 7% by 3 years and 2 months. What is the compound interest?
  • 11. Example 3: Accumulate P 16,000 in 16 months at 16% semi-annually.