An investor can invest money with a particular bank and earn a stated interest r

Question

An investor can invest money with a particular bank and earn a stated interest rate of 6.60%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity? Interest Rates Nominal rate Periodic rate Effective annual rate 6.60% 1.65% Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 6%. But the bank is compounding semiannually. What is the effective interest rate that Rahul would pay for the loan? o 6.090% o 6.404% o 6.211% 5.996% Another bank is also offering favorable terms, so Rahul decides to take a loan of $22,000 from this bank. He signs the loan contract at 8% compounded daily for three months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.) O $23,342.42 O $22,893.52 O $22,444.63 $21,771.29

Explanation / Answer

1.

The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate

So if nominal interest rate (i), number of compounding in a year is (m), effective interest will be

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 6.6% per year

Number of compounding in a year (m) = 4

Let's put all the values in the formula

Effective interest rate = (1 + 0.066/4) ^4 - 1

                                              = (1 + 0.0165) ^4 - 1

                                              = (1.0165) ^4 - 1

                                              = 1.06765 - 1

                                              = 0.0677

So annual effective interest rate is 6.77% per year

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Nominal interest rate (i) = 6% per year

Number of compounding in a year (m) = 2

Let's put all the values in the formula

Effective interest rate = (1 + 0.06/2) ^2 - 1

                                              = (1 + 0.03) ^2 - 1

                                              = (1.03) ^2 - 1

                                              = 1.0609 - 1

                                              = 0.0609

So annual effective interest rate is 6.09% per year

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