First National Bank offers two-year CDs at 9.16% compounded daily, and Citywide Savings offers two-year CDs at 9.17% compounded quarterly. Compute the annual yield for each institution. (Round your answers to two decimal places.)
Question
First National Bank offers two-year CDs at 9.16% compounded daily, and Citywide Savings offers two-year CDs at 9.17% compounded quarterly. Compute the annual yield for each institution. (Round your answers to two decimal places.)
Solution
To calculate the annual yield for each institution, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For First National Bank:
- r = 9.16% = 0.0916 (in decimal)
- n = 365 (compounded daily)
- t = 2 years
The annual yield can be calculated as follows:
A = P(1 + r/n)^(nt) A = P(1 + 0.0916/365)^(365*2)
We are interested in the annual yield, so we set P = 1 (as if we invested one unit of currency). Therefore:
A = 1(1 + 0.0916/365)^(365*2)
For Citywide Savings:
- r = 9.17% = 0.0917 (in decimal)
- n = 4 (compounded quarterly)
- t = 2 years
The annual yield can be calculated as follows:
A = P(1 + r/n)^(nt) A = P(1 + 0.0917/4)^(4*2)
Again, we set P = 1:
A = 1(1 + 0.0917/4)^(4*2)
Now, you can calculate the values of A for each bank, which will give you the annual yield for each institution. Remember to round your answers to two decimal places.
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