The number of compounding periods in one year is called comp

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows. 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% 6.77% | 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? 6.090% o 6.175% O 6.404% O 6.211% Another bank is also offering favorable terms, so Rahul decides to take a loan of $20,000 from this bank. He signs the loan contract at 12% compounded daily for six 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 $21,236.52 $22,085.98 O $20,811.79 O $21,661.25 Session Timeout 51:27

Solution

Question 1

1) Nominal Rate: It is the interest rate before taking inflation into account.It is normally the stated interest in loan.

In this case, Bank has a stated interest of 6.6%. Therefore, Nominal rate = 6.60%

2) Periodic Rate: It is the interest rate per period. It can be calculated as

nominal rate / no. of compounding periods

6.60 / 4

= 1.65%

3) Effective Annual Rate: It is the actual interest earned or paid. It can be calculated as

[1+(stated annual interest rate/no. of compounding periods)]^{no. of compounding periods}-1

[1+(.660/4)]⁴-1

=[1+0.0165]⁴-1

= 1.0677-1

Effective Annual Rate = 6.77%

Question 2

Effective Annual Rate = [1+(stated annual interest rate/no. of compounding periods)]^{no. of compounding periods}-1

= [1+(.06/2)]²-1

= 1.03²-1

= 1.0609 - 1

= 6.090% (option 1)

Question 3

Future Value = Loan amount * (1+rate per period)^{no. of periods}

= 20,000 * (1 + (.12/365))^6*365/12

= 20,000 * 1.061826

= $21,236.52