Question

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 4.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Interest Rates
Nominal rate 4.40%
Periodic rate 1.10%
Effective annual rate 4.47%
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 4%. But the bank is compounding daily. What is the effective interest rate that Rahul would pay for the loan?
a. 4.081%
b. 4.202%
c. 3.959%
d. 4.395%
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 9% compounded daily for nine 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.)
a. $24,477.81
b. $24,948.54
c. $23,536.36
d. $24,007.09

Answer 1

1. a. 4.081%

2. c. $23,536.36

Step-by-step explanation:

1. Periodic rate=(4.4%/4) = 1.1%

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

where m=compounding periods

= (1+0.044/4)^4-1

= 1.011^4 - 1

= 1.04473133864 - 1

= 0.04473133864

= 4.47%

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

where m=compounding periods

=(1+0.04/365)^365-1

= (1+0.00010958904)^365 - 1

= 1.00010958904^365 - 1

= 1.04080849272 - 1

= 0.04080849272

= 4.081%

2. A=P(1+r/365)^365*n

where A=future value, P=present value, r=rate of interest, n=time period.

= 22000*(1+9%/365)^(9/12*365)

= $23,536.36