Question

Your bank is offering you an account that will pay 18 % interest​ (an effective​ two-year rate) in total for a​ two-year deposit. Determine the equivalent discount rate for the following​periods:

a. Six months
The equivalent discount rate for a period length of six months is ____% ???
b. One year
The equivalent discount rate for a period length of one year is_____%???
c. One month ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)
The equivalent discount rate for a period length of one month is_____%???

Answer 1

To find equivalent discount rates for different periods, the effective two-year rate of 18% is first converted into an equivalent annual rate, and from that, discount rates for six months, one year, and one month can be calculated using the appropriate formulas.

Step-by-step explanation:

The student's question involves converting an effective two-year rate of 18% into equivalent discount rates for different time periods: six months, one year, and one month. To find the equivalent discount rates for these periods, we use the formula for converting an effective annual rate (EAR) to a discount rate for a given period, taking into account the compounding effect:

d = 1 - (1 + r)-t

Where d is the discount rate, r is the interest rate, and t is the time period as a fraction of the year. Since the given effective two-year rate is 18%, first we must find the equivalent annual rate (EAR) using the formula:

EAR = (1 + i)1/n - 1

Calculating the EAR for biannual, annual, and monthly periods and then converting to the equivalent discount rates will give us the requested values.