A car dealership is currently offering interest rates of 12% p.a. compounding quarterly. What is the effective semi-annual rate?Group of answer choices3%0.9902%6.09%0.2276%12.5509%

To calculate the effective semi-annual rate from a quarterly compounding rate, we first need to find the quarterly rate and then compound it for two quarters (which is equivalent to a semi-annual period).

1. The nominal interest rate is 12% per annum. Since it's compounded quarterly, we divide this by 4 to get the quarterly rate. So, 12% / 4 = 3%.

2. Now, we need to compound this quarterly rate for two quarters to get the semi-annual rate. The formula for compound interest is A = P(1 + r/n)^(nt), where:

   • A is the amount of money accumulated after n years, including interest.
   • P is the principal amount (the initial amount of money).
   • r is the annual interest rate (in decimal).
   • n is the number of times that interest is compounded per year.
   • t is the time the money is invested for in years.

In this case, we're looking for the effective semi-annual rate, so we're interested in the (1 + r/n)^(nt) part of the formula. We know that r = 3% (or 0.03 in decimal form), n = 1 (since we're compounding once per quarter), and t = 2 (since two quarters make a semi-annual period).

So, we have (1 + 0.03/1)^(1*2) = (1.03)^2 = 1.0609.

3. To convert this back into a percentage and subtract the principal, we subtract 1 and multiply by 100. So, (1.0609 - 1) * 100 = 6.09%.

So, the effective semi-annual rate is 6.09%.