10.4k views
3 votes
Your bank is offering you an account that will pay 23% 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
b. One year
c. One month
(Note: Be careful not to round any intermediate steps less than six decimal places.) a. Six months The equivalent discount rate for a period length of six months is %. (Round to two decimal places.)

User Detly
by
8.2k points

1 Answer

5 votes

Final answer:

To find the equivalent six-month discount rate from an effective 23% two-year interest rate, we first determine the annual compound rate and then adjust it to a six-month period. Maintaining precision in all intermediate calculations before rounding the final discount rate to two decimal places is crucial for accuracy.

Step-by-step explanation:

The question is related to finding the equivalent discount rate for different time periods when given an effective interest rate over two years. We have an effective two-year interest rate of 23%. To convert this effective interest rate into equivalent discount rates for shorter periods (six months, one year, etc.), we will need to use the formula for equivalent interest rates.

First, we find the annual compound interest rate (r) that would result in a 23% increase over two years. This compound rate is calculated using the formula (1 + r)^2 = 1 + 0.23, which gives us r after solving for it.

Once we have the annual rate, we need to adjust this rate to different periods. For a six-month period, we would divide the annual rate by 2. But to find the discount rate, we must reverse-engineer this process. We use the formula (1 - d) = (1/(1 + r/2)), where r is the annual compound interest rate and d is the six-month discount rate.

To compute the six-month discount rate precisely, maintain all intermediate steps to at least six decimal places before rounding the final percentage discount to two decimal places to ensure accuracy.

User Gabethegrape
by
8.3k points