Interest Formula for Varying Time Units and Compoundings?

In summary, the formula A=A0(1+r/k)^(kt) can be used for any time interval, but the units of r and k must match the basic time interval used in the formula. It is common to change time units in applications, but the interest rate must also be adjusted accordingly.
  • #1
member 508213
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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  • #2
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.
 
  • #3
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.
 

1. What is the interest formula?

The interest formula is a mathematical equation used to calculate the amount of interest earned or paid on a loan or investment. It takes into account the principal amount, interest rate, and time period to determine the total interest amount.

2. How do I calculate the interest using the formula?

To calculate interest, you will need to know the principal amount, interest rate, and time period. The formula is: Interest = (Principal * Interest Rate * Time)/100. This will give you the total interest amount in dollars.

3. What is the difference between simple and compound interest?

Simple interest is calculated only on the initial principal amount, whereas compound interest is calculated on both the initial principal and any accumulated interest. This means that compound interest will earn more over time compared to simple interest.

4. Can the interest formula be used for any type of loan or investment?

Yes, the interest formula can be used for any type of loan or investment as long as the interest rate is expressed as a percentage and the time period is in years. It is a universal formula that can be applied to different scenarios.

5. How does the time period affect the interest amount?

The longer the time period, the higher the interest amount will be. This is because the interest is calculated over a longer period of time, resulting in more interest earned. Additionally, for compound interest, the more frequent the compounding periods (e.g. monthly instead of yearly), the higher the interest amount will be.

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