3. The Lagelleys have $25,000 that they want to invest in a certificate of deposit. Granite Trust offers a 4-year
certificate of deposit that earns interest at 3.50%
compounded quarterly. Hancock Cooperative Bank offers
a 4-year certificate that earns interest at 3.25%
compounded daily. a) Which CD earns more interest? b)
By
how much?



Answer :

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.