a government bod pays 100 in a year at a discount rate of 5%(assume simple interest). How much did the bond cost? What is the annual percentage rate? Should it be more or less than 5%?
To calculate the cost of the bond, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the interest is $100, and the rate is 5%, the formula can be rearranged to solve for the principal:
Principal = Interest / (Rate * Time)
Since the time period is not specified, we assume it to be 1 year. Hence:
Principal = $100 / (0.05 * 1) = $2000
So, the bond cost $2000.
To determine the annual percentage rate (APR), we can use the formula:
APR = (Interest / Principal) * (1 / Time) * 100
Substituting the given values:
APR = ($100 / $2000) * (1/1) * 100 = 5%
The APR in this case is 5%, which is the same as the discount rate. The simple interest rate and APR are the same when the time period is 1 year.
So, the APR for this bond is 5%. The discount rate should be equal to the APR in this case since it is a simple interest bond.