Answer:
What is the total amount = $3456
What is the compound interest = $2432.
Explanation:
To find the total amount after three years, we first need to calculate the interest earned in each half-yearly period:
Interest for 1st half-yearly period = (50/100 * 1024) = $512
Interest for 2nd half-yearly period = (50/100 * (1024 + 512)) = $768
Interest for 3rd half-yearly period = (50/100 * (1024 + 512 + 768)) = $1152
The amount after the first half-yearly period is:
Amount after 1st half-yearly period = Principal + Interest for 1st half-yearly period
= $1024 + $512
= $1536
The amount after the second half-yearly period is:
Amount after 2nd half-yearly period = Amount after 1st half-yearly period + Interest for 2nd half-yearly period
= $1536 + $768
= $2304
The amount after the third half-yearly period is:
Amount after 3rd half-yearly period = Amount after 2nd half-yearly period + Interest for 3rd half-yearly period
= $2304 + $1152
= $3456
Therefore, the total amount after three years, compounded half-yearly, is $3456.
To calculate the compound interest, we subtract the principal amount from the total amount:
Compound interest = Total amount - Principal
= $3456 - $1024
= $2432
Therefore, the compound interest is $2432.