Question

A bank is offering to sell 3-month certificates of deposit for $15,250. At the end of 3 months, the bank will pay $16,000 to the certificate owner. Calculate the rates and follow formatting as described below:______.

(The interest rates should be rounded to two decimal Places.
Example: 2.347 will be rounded to 2.35; no% sign should be entered, Example: 3.19 is correct but 3.19% is not correct)
1. Interest rate per compounding period is:_______.
2. The nominal annual interest rate is:________.
3. The effective annual interest rate is:________.

Answer 1

i= 4.92% compounded quarterly

Nominal rate= 19.68%

Effective interest rate= 21.18%

Step-by-step explanation:

Giving the following information:

PV= 15,250

FV= 16,000

n= 3 months

First, we need to calculate the interest rate for a quarter:

i= (FV - PV) / PV

i= (16,000 - 15,250) / 15,250

i= 0.0492 = 4.92% compounded quarterly

Now, we can determine the annual nominal rate:

Nominal rate= i*number of periods

Nominal rate= 0.0492*4= 0.1968= 19.68%

Finally, the effective annual interest rate:

Effective interest rate= [(1+i)^n] - 1

Effective interest rate= (1.0492^4) - 1

Effective interest rate= 0.2118 = 21.18%