Use the digits of your birthday as the amount of your initial investment (i.e., 6/25 is $625), calculate the value of this investment after 10 years at 3.5% APR for interest compounded yearly, quarterly, monthly, and daily. What do you notice?
more frequent compounding, more money.
To calculate the value of your initial investment after 10 years at different compounding frequencies, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = initial investment
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we will use the digits of your birthday as the amount of your initial investment.
Let's assume your birthday is on June 25th, therefore your initial investment is $625.
Now, let's calculate the value of this investment after 10 years at different compounding frequencies:
1. Yearly compounding:
A = $625(1 + 0.035/1)^(1*10)
A ≈ $864.89
2. Quarterly compounding:
A = $625(1 + 0.035/4)^(4*10)
A ≈ $866.73
3. Monthly compounding:
A = $625(1 + 0.035/12)^(12*10)
A ≈ $867.70
4. Daily compounding:
A = $625(1 + 0.035/365)^(365*10)
A ≈ $867.75
What we notice is that as the compounding frequency increases, the value of the investment also increases. This is because in more frequent compounding, the interest is added more frequently and earns interest on interest more often.
In this specific example, the differences in the final amounts are relatively small, but over longer periods or with higher interest rates, the differences can become more significant.