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

See previous post for solution.

To calculate the value of the two accounts at the end of the year, we need to use the formulas for compound interest.

For Bank A, which offers an annual interest rate of 3% compounded semiannually, we use the formula:

A = P(1 + r/n)^(n*t)

Where:
A = the final amount
P = the principal (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, the principal (P) is $12,000, the annual interest rate (r) is 3% (or 0.03 as a decimal), interest is compounded semiannually (n = 2), and the time period (t) is 1 year.

Using these values, we can calculate the final amount for Bank A:

A = 12000(1 + 0.03/2)^(2*1)
= 12000(1 + 0.015)^2
≈ 12000(1.015)^2
≈ 12000(1.030225)
≈ $12,362.70

Now, let's calculate the value of the account at Bank B, which offers an annual interest rate of 2.75% compounded continuously.

For continuous compounding, the formula is:

A = P * e^(r*t)

Where:
A = the final amount
P = the principal (initial deposit)
r = the annual interest rate (expressed as a decimal)
t = the number of years
e = the mathematical constant approximately equal to 2.71828

Using the same values as before, we can calculate the final amount for Bank B:

A = 12000 * e^(0.0275*1)
≈ 12000 * e^(0.0275)
≈ 12000 * 1.027915
≈ $12,334.98

Therefore, at the end of the year, the account at Bank A would be approximately $12,362.70, while the account at Bank B would be approximately $12,334.98.

Based on the calculations, I would recommend choosing Bank A as it offers a higher return on your investment at the end of the year.