Mabel has $35,000 to invest in a certificate of deposit for 4 years. The certificate of deposit earns interest at 4.75% compounded daily. What is the annual percentage yield to the nearest thousandth of a percent?
All we need is the 4.75% per annum compounded daily
Let the equivalent annual rate be i
1+i = (1 + .0475/365)^365
1+i = 1.0486429...
So the annual rate is 4.864 %
To find the annual percentage yield (APY) for the certificate of deposit, we need to use the formula:
APY = (1 + r/n)^n - 1
Where:
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
In this case, the annual interest rate is 4.75% (or 0.0475 as a decimal), and the interest is compounded daily, so n = 365.
Now, let's calculate the APY:
APY = (1 + 0.0475/365)^365 - 1
To find the value of the expression inside the parentheses, we can use a calculator or spreadsheet software.
(1 + 0.0475/365)^365 = 1.0481736514
Now, subtract 1 from this result:
APY = 1.0481736514 - 1 = 0.0481736514
The APY is approximately 0.0481736514.
To convert this to a percentage, we multiply by 100:
APY = 0.0481736514 * 100 = 4.81736514
Rounding this to the nearest thousandth of a percent, the annual percentage yield is approximately 4.817%.