To determine the amount Bob would have gained by interest, we need to calculate the compound interest for each deposit and then add them together.

Step 1: Calculate the interest for the first deposit on 15th June.
The formula for compound interest is: A = P(1 + r/n)^(nt), where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (5% in this case)
n = number of times interest is compounded per year (2, since it is biannual)
t = number of years

For the first deposit on 15th June, the principal amount is $3200, the annual interest rate is 5%, the number of times interest is compounded per year is 2, and the number of years is 1/2 (since it is a biannual deposit).

Using the formula, we can calculate the final amount (A) for the first deposit:
A = 3200(1 + 0.05/2)^(2 * 1/2)
A = 3200(1 + 0.025)^(1)
A = 3200(1.025)
A = 3280

So, the first deposit on 15th June would have gained $80 in interest.

Step 2: Calculate the interest for the second deposit on 15th December.
Using the same formula, we can calculate the final amount (A) for the second deposit:
A = 3200(1 + 0.05/2)^(2 * 1/2)
A = 3200(1 + 0.025)^(1)
A = 3200(1.025)
A = 3280

So, the second deposit on 15th December would have also gained $80 in interest.

Step 3: Calculate the total interest gained.
To determine the total interest gained, we simply add the interest gained from both deposits:
Total interest = $80 + $80 = $160

Therefore, Bob would have gained $160 by interest from his deposits.

Question

To determine the amount Bob would have gained by interest, we need to calculate the compound interest for each deposit and then add them together.

Step 1: Calculate the interest for the first deposit on 15th June.
The formula for compound interest is: A = P(1 + r/n)^(nt), where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (5% in this case)
n = number of times interest is compounded per year (2, since it is biannual)
t = number of years

For the first deposit on 15th June, the principal amount is $3200, the annual interest rate is 5%, the number of times interest is compounded per year is 2, and the number of years is 1/2 (since it is a biannual deposit).

Using the formula, we can calculate the final amount (A) for the first deposit:
A = 3200(1 + 0.05/2)^(2 * 1/2)
A = 3200(1 + 0.025)^(1)
A = 3200(1.025)
A = 3280

So, the first deposit on 15th June would have gained $80 in interest.

Step 2: Calculate the interest for the second deposit on 15th December.
Using the same formula, we can calculate the final amount (A) for the second deposit:
A = 3200(1 + 0.05/2)^(2 * 1/2)
A = 3200(1 + 0.025)^(1)
A = 3200(1.025)
A = 3280

So, the second deposit on 15th December would have also gained $80 in interest.

Step 3: Calculate the total interest gained.
To determine the total interest gained, we simply add the interest gained from both deposits:
Total interest = $80 + $80 = $160

Therefore, Bob would have gained $160 by interest from his deposits.

Knowee AI · Accepted Answer