Question

Find the effective interest rate of 12% compounded quarterly (round to nearest hundred) a) 10.12% b) 12.55% c) 12.15% d) 12.50% e) None of these

Answer 1

the effective interest rate is approximately 12.50%, so the correct answer is (d) 12.50%.

Explanation:

Answer 2

(b) 12.55%

Explanation:

The effective interest rate, also known as the annual equivalent rate (AER) or annual percentage rate (APR), represents the true annual cost of borrowing or the actual yield on an investment, taking into account compounding interest over a specified period.

The formula to calculate the effective interest rate for a given nominal interest rate compounded n times per year is:

`AER = \left(1 + (r)/(n)\right)^n - 1`

where:

• r is the nominal interest rate (as a decimal),
• n is the number of compounding periods per year.

In this case:

• r = 12% = 0.12
• n = 4 (compounded quarterly)

Substitute these values into the formula and solve for AER:

`AER = \left(1 + (0.12)/(4)\right)^4 - 1`

`AER = \left(1 + 0.03\right)^4 - 1`

`AER = \left(1.03\right)^4 - 1`

`AER = 1.12550881 - 1`

`AER = 0.12550881`

Converting this to a percentage and rounding to the nearest hundredth gives:

`AER \approx 12.55\%`

Therefore, the effective interest rate is 12.55%.