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 β $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 β $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.