Interest Formula for Varying Time Units and Compoundings?

[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?

 

[Mark44]

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.

 

[pwsnafu]

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.