you are looking for a safe place to put 30,000.00 for one yr. Bank A offers 2.46% interest rate continuously. Bank B offers 2.48% quarterly and Bank C offers 2.47% monthly. Find the most effective rate of each to determine which would earn you the most interest at the end of one yr.
Bank A interest per years = (2.46*30000)/100= $738 per year
Bank B interest (2.48*30000)/100=744
Bank c interest (2.47*30000)/100=741
So Bank B the most interest at the end of one year.
John, please do not attempt to answer questions, if you have no idea how that question is done.
Bank A ---> 30000 e^(.0246) = $30,747.15
Bank B ---> 30000(1 + .0248/4)^4 = $30,750.95
Bank C ---> 30000(1+.0247/12)^12 = $30,749.45
Plan B is the best way, but not for the "reasons" John gave. He didn't even include the compounding factor.
To determine which bank would earn you the most interest at the end of one year, we need to compare the effective rates offered by Bank A, Bank B, and Bank C. The effective rate takes into account the compounding frequency and gives us an annualized rate of interest.
Let's first calculate the effective rate for Bank A, which offers a continuously compounded interest rate of 2.46%. The formula for calculating continuous compounding is:
Effective interest rate = (1 + i/t)^(t*n) - 1
Where i is the interest rate, t is the number of times interest is compounded per year, and n is the number of years. In this case, since we want to calculate the effective rate for one year, n would equal 1.
For Bank A:
i = 2.46% = 0.0246
t = Continuous compounding
n = 1
Since Bank A offers a continuously compounded interest rate, we can plug in the values into the formula and find the effective rate:
Effective interest rate for Bank A = (1 + 0.0246/1)^(1*1) - 1
Simplifying the equation, we get:
Effective interest rate for Bank A = (1.0246)^1 - 1
Now let's calculate the effective rates for Bank B and Bank C using a similar approach.
For Bank B, which offers a quarterly compounded interest rate of 2.48%:
i = 2.48% = 0.0248
t = 4 (since interest is compounded quarterly, there are four compounding periods in a year)
n = 1
Effective interest rate for Bank B = (1 + 0.0248/4)^(4*1) - 1
For Bank C, which offers a monthly compounded interest rate of 2.47%:
i = 2.47% = 0.0247
t = 12 (since interest is compounded monthly, there are twelve compounding periods in a year)
n = 1
Effective interest rate for Bank C = (1 + 0.0247/12)^(12*1) - 1
By evaluating these equations, you will find the effective interest rates for each bank.
Comparing the effective interest rates obtained for Bank A, Bank B, and Bank C, the bank with the highest effective rate will be the one that earns you the most interest at the end of one year.