ohn offers 5% compound interest to Bob on a biannual basis. Bob deposits 3200 dollars each on 15th June and 15th December of a year. Determine the amount Bob would have gained by interest.6642332136424642

Sure, let's calculate the amount Bob would have gained by interest step by step.

Step 1: Calculate the interest rate per period The interest rate offered by John is 5% per period. Since the interest is compounded biannually, we need to divide the annual interest rate by 2. Therefore, the interest rate per period is 5% / 2 = 2.5%.

Step 2: Calculate the number of periods Bob deposits $3200 on 15th June and 15th December of a year. Since the interest is compounded biannually, there are 2 periods in a year.

Step 3: Calculate the future value of each deposit To calculate the future value of each deposit, we can use the compound interest formula:

Future Value = Principal * (1 + Interest Rate)^Number of Periods

For the first deposit on 15th June, the future value would be: Future Value = $3200 * (1 + 2.5$3200 * (1 + 0.025)^2 = $3200 * (1.025)^2 =$3200 * 1.050625 = $3361.60

For the second deposit on 15th December, the future value would be: Future Value = $3200 * (1 + 2.5$3200 * (1 + 0.025)^2 = $3200 * (1.025)^2 =$3200 * 1.050625 = $3361.60

Step 4: Calculate the total amount gained by interest To calculate the total amount gained by interest, we need to sum up the future values of both deposits:

Total Amount Gained = Future Value of the first deposit + Future Value of the second deposit Total Amount Gained = $3361.60 +$3361.60 = $6723.20

Therefore, Bob would have gained $6723.20 by interest.