You receive $12,000 and looking for a bank to deposit the funds. Bank A offers an account with an annual interest rate of 3% compounded semiannually. Bank B offers an account with 2.75% annual interest rate compounded continuously. Calculate the value of the two accounts at the end of the year and recommend

Pt = Po(1+r)^n.

BANK A:
r = (3 %/2) / 100 % = 0.015 = Semi-annual rate expresed as a decimal.

n = 2 comp / yr + 1yr = 2 compounding
periods.

Pt = 12,000(1.015)^2 = $12362.70.

BANK B: Pt = Po*e^rt.

r = 2.75% / 100% = 0.0275 = Annual %
rate expressed a a decimal.

rt = 0.0275 /yr * 1 yr = 0.0275.

Pt = 12000*e^0.0275 = $12,334.58.

To calculate the value of the two accounts at the end of the year and make a recommendation, we need to use the compound interest formula for each bank account.

For Bank A, with an annual interest rate of 3% compounded semiannually:
The formula to calculate the future value (A) is:
A = P(1 + r/n)^(nt)

Where:
P = Principal amount ($12,000)
r = Annual interest rate (3% or 0.03)
n = Number of times interest is compounded per year (2 for semiannually)
t = Number of years (1 year)

Plugging in the values:
A = 12000(1 + 0.03/2)^(2*1)
A = 12000(1 + 0.015)^2
A ≈ $12,361.50

For Bank B, with a continuous compounding interest rate of 2.75%:
The formula to calculate the future value (A) is:
A = P * e^(rt)

Where:
P = Principal amount ($12,000)
r = Annual interest rate (2.75% or 0.0275)
t = Number of years (1 year)
e = Euler's number (approximately 2.71828)

Plugging in the values:
A = 12000 * e^(0.0275*1)
A ≈ $12,326.57

Therefore, the approximate values of the two accounts at the end of the year are:
- Bank A: $12,361.50
- Bank B: $12,326.57

Based on the calculations, Bank A would yield a slightly higher value at the end of the year compared to Bank B. So, my recommendation would be to choose Bank A to deposit your funds.