Chapter 4: Aplia Homework The number of compounding periods in one year is calle

Question

Chapter 4: Aplia Homework 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 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% 0 6.175% Q 5.996% 6.267% Another bank is also offering favourable terms, so Rahul decides to take a loan of $12,000 from this bank. He signs the loan contract at 7% compounded daily for four months. Based on a 365-day year, what is the total amount that

Explanation / Answer

Interest rate = 6.60% compounded quaterly

Periodic interest rate = nominal rate/number of times compounded in year

=6.60/4 = 1.65%

EAR=(1+i/m)^m - 1

EAR = effective annual interest rate , i= nominal rate and , m= number of compounding periods

EAR=(1+0.066/4)^4-1

=0.06765

=6.76%

2) EAR=(1+i/m)^m - 1

EAR = effective annual interest rate , i= nominal rate and, m= number of compounding periods

i=6% =0.06

m=2

EAR=(1+0.06/2)^2 -1 =0.0609 =6.090%(Answer)

3) nominal rate=7%=0.07

loan amount=$12,000

compounded daily

loan period=4months

number of days in 3 months=(365/12)*4= 121.67 days

loan rate on daily basis=0.07/365=0.00019178

final loan amount = amount of loan taken*(1+r)^n

Loan Amount:

=$12000*(1+0.00019178)^121.67

=12,283.27

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