Determine the annual percentage yield or the effective interest rate for $700 invested at 3.27% over 9 years compounded daily
The formula to calculate the annual percentage yield (APY) or effective interest rate for a given investment is:
APY = (1 + (r/n))^(n) - 1
where:
- r is the annual interest rate (3.27% or 0.0327),
- n is the number of compounding periods per year (365 for daily compounding),
- t is the number of years the money is invested for (9 years), and
- APY is the annual percentage yield or effective interest rate.
Plugging in the values, we get:
APY = (1 + (0.0327/365))^(365*9) - 1
APY = (1 + 0.0000896)^(3285) - 1
APY = (1.0000896)^(3285) - 1
APY = 1.31884 - 1
APY = 0.31884 or 31.884%
Therefore, the annual percentage yield or effective interest rate for $700 invested at 3.27% over 9 years compounded daily is 31.884%.