Find the Effective Rate?

Find the effective rate of interest for 5.25% compounded quarterly.

ALSO:

What is meant by EFFECTIVE RATE?

Find the Effective Rate?

effective rate is the rate if the conversion period is one year:

thus

(1+i) = (1 + {0.0525/4})^4.

solve for i.

(1+i) =(1.013125)^4

(1+i) =1.05354267

i = 5.35%

d:

Find the Effective Rate?

The simple interest rate that generates the same amount of interest in one year as a given compound interest rate is called the effective interest rate, or, annual percentage yield (APY) for an investment, or, annual percentage rate (APR) for a loan.

Find the Effective Rate?

5.25% annual rate will equal 5.354% when compounded quarterly

annual rate = 5.25%

APY (annual percentage yield) = 5.354%

(1+(.0525/4))^4 - 1 = .05354 = 5.354%

Find the Effective Rate?

Assume you put in 10,000,000 into the account.

The rate in 5.25% compounded quarterly, so each quarter the interest is 5.25%/4 = 1.3125%.

The first quarter you began with 10,000,000.00 and got 1.3125% interest, so you have 10,131,250.00 at the end of the first quarter. At the end of the second quarter, you receive interest on the whole amount you began that quarter with, so you have 10,264,222.66. At the end of the third quarter you have 10,398,940.58, and at the end of the fourth quarter you have 10,535,426.67.

The interest you get is 535,426.67. This is about 5.3543%, so that is the effective rate.