Question

You have $5,600 that you want to use to open a savings account. There are five banks located in your area. The rates paid by banks A through E, respectively, are given below. Which bank should you select if your goal is to maximize your interest income?

Answer 1

Answer:

It would be best to pick the annual rate as is the higher maong the given choised.

bank rates:

3.26 percent, compounded annually

3.20 percent, compounded monthly

3.25 percent, compounded semi-annually

3.10 percent, compounded continuously

3.15 percent, compounded quarterly

Explanation:

we move the rates to annual and check the effective rate:

$(1+r_n/m)^{m} -1 = r_e$

$(1+0.032/12)^{12} -1 = r_e\\r_e = 0.03247353(1+0.0325/2)^{2} -1 = r_e\\\\r_e = 0.03530625$

continuos rate:

$e^{0.0310} -1 = r_e\\r_e = 0.031485504$

3.15 quarterly:

$(1+r_n/m)^{m} -1 = r_e$

0.0318740511

Answer 2

Options:[

A. 3.26 percent, compounded annually

B. 3.20 percent, compounded monthly

C. 3.25 percent, compounded semi-annually

D. 3.10 percent, compounded continuously

E. 3.15 percent, compounded quarterly

Answer:

C) 3.25 percent, compounded semi-annually

Explanation:

Usually the higher interest rate, the more money you will earn. But the frequency at which the interest rate is compounded may change the equation. Usually the shorter the compounding frequency, the higher the interest rate. E.g. a 10% compounded semi-annually yields 10.25% annually, but 10% compounded monthly yields 10.47%

we must determine the effective yearly interest rates:

• 3.26 percent, compounded annually  = 3.26% annual
• 3.20 percent, compounded monthly  = 3.25% annual
• 3.25 percent, compounded semi-annually  = 3.28% annual
• 3.10 percent, compounded continuously (daily basis) = 3.15%
• 3.15 percent, compounded quarterly = 3.19%

Since option C yields the highest effective yearly interest rate, that is the bank that you should choose.

*the formula for determining the effective interest rate = (1 + r/n)ⁿ, e.g. semi-annual n = 2