Interest Formula for Varying Time Units and Compoundings?

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SUMMARY

The formula A=A0(1+r/k)^(kt) is versatile and does not strictly require t to be in years or k to represent annual compounding. While traditionally used with annual time intervals, both r and k can be adapted to different time units, provided that the interest rate is adjusted accordingly. For example, in a scenario with quarterly compounding, one can redefine the time unit to 9 months with three compoundings per unit, demonstrating the formula's flexibility in practical applications.

PREREQUISITES
  • Understanding of the compound interest formula A=A0(1+r/k)^(kt)
  • Knowledge of interest rates and their units
  • Familiarity with time intervals and their conversions
  • Basic financial mathematics
NEXT STEPS
  • Research how to adjust interest rates for different compounding periods
  • Learn about financial modeling using varying time units
  • Explore examples of compound interest calculations with non-annual compounding
  • Study the implications of different compounding frequencies on investment growth
USEFUL FOR

Finance students, financial analysts, and anyone involved in investment planning or financial modeling who needs to understand the implications of varying time units and compounding frequencies on interest calculations.

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For the formula A=A0(1+r/k)^(kt) does it only work if t is in years and k is how many times per year it is compounded?
 
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Austin said:
For the formula A=A0(1+r/k)^(kt) does it only work if t is in years and k is how many times per year it is compounded?
No, I believe that r and k and t could be defined in terms of some different time interval, but I have only ever seen this formula used when the basic time interval is the year. The units of r are typically in terms of the interest in a year, k is usually the number of interest computing periods per year, and t is the number of years.
 
Austin said:
For the formula A=A0(1+r/k)^(kt) does it only work if t is in years and k is how many times per year it is compounded?

No, t is the time in time units (whatever that is) and k is the number of compoundings per time unit. Changing time units is common in applications, but you also need to change the interest rate to match the time unit.

Example: consider the problem of depositing $25 in Jan, Apr and Jul. Then $50 in Oct, Jan and Apr. Then $75 in Jul, Oct, Jan, and so on. Keep this pattern for 12 years. Suppose compounding is quarterly. The best way to tackle the problem is to change the time unit into 9 months and three compoundings per time unit.
 

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