Answer:
For CD 1:
Interest Rate (r) = 3.50% = 0.035
Compounding Period (n) = Quarterly
Time (t) = 4 years
For CD 2:
Interest Rate (r) = 3.25% = 0.0325
Compounding Period (n) = Daily
Time (t) = 4 years
We'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount after interest
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal)
n = Number of times the interest is compounded per year
t = Time the money is invested for in years
Let's calculate the total amount for each CD:
For CD 1:
P = Principal amount
r = 0.035
n = 4 (quarterly)
t = 4 years
For CD 2:
P = Principal amount
r = 0.0325
n = 365 (daily)
t = 4 years
Let's calculate:
For CD 1:
A1 = P(1 + 0.035/4)^(4*4)
A1 = P(1.00875)^16
For CD 2:
A2 = P(1 + 0.0325/365)^(365*4)
A2 = P(1.000089041)^1460
To compare which CD earns more interest, we'll assume an initial deposit of $1 for simplicity.
For CD 1:
A1 = (1)(1.00875)^16
A1 ≈ 1.154058
For CD 2:
A2 = (1)(1.000089041)^1460
A2 ≈ 1.13546
a) CD 1 earns more interest.
b) The difference in interest earned between CD 1 and CD 2 is approximately:
Difference = A1 - A2
Difference ≈ 1.154058 - 1.13546
Difference ≈ 0.018598
So, CD 1 earns approximately $0.018598 more interest than CD 2 over the 4-year period.
