Determine the annual percentage yield, or the effective interest rate, for $700 invested at 4.29% over 14 years compounded daily. Round your answer to the nearest hundredth of a percent, if necessary.
To calculate the annual percentage yield for $700 invested at 4.29% over 14 years compounded daily, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case:
P = $700
r = 4.29% or 0.0429
n = 365 (compounded daily)
t = 14 years
Plug these values into the formula:
A = 700(1 + 0.0429/365)^(365*14)
A = 700(1 + 0.0001175)^5110
A = 700(1.0001175)^5110
A = 700(1.670926)
A = $1,171.65
Now, we can calculate the effective annual interest rate using the formula:
APY = (1 + r/n)^n - 1
APY = (1 + 0.0429/365)^365 - 1
APY = (1.0001175)^365 - 1
APY = 1.0456517 - 1
APY = 0.0456517
The annual percentage yield is 4.57% (rounded to the nearest hundredth of a percent).