Find the difference in financial gains when $3,200 is invested for 8 years with an interest rate of 4.5% for both simple interest and compound interest, and interest is compounded annually. (1 point)
$1,350.72
$231.57
$198.72
$47,810.80
To find the difference in financial gains between simple interest and compound interest, we need to calculate the amount of money earned through both methods.
For simple interest, we use the formula: A = P(1 + rt), where A is the total amount, P is the principal (initial investment), r is the interest rate, and t is the time period.
For the given investment of $3,200 at an interest rate of 4.5%, the total amount after 8 years with simple interest is:
A = 3200(1 + (0.045)(8))
A = 3200(1 + 0.36)
A = 3200(1.36)
A = $4352
The financial gain through simple interest is $4352 - $3200 = $1152.
For compound interest, we use the formula: A = P(1 + r/n)^(nt), where A is the total amount, P is the principal (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.
Since interest is compounded annually, n = 1. Plugging in the values:
A = 3200(1 + (0.045)/1)^(1*8)
A = 3200(1 + 0.045)^8
A = 3200(1.045)^8
A = $4350.72
The financial gain through compound interest is $4350.72 - $3200 = $1150.72.
The difference in financial gains between simple interest and compound interest is $1152 - $1150.72 = $1.28.
Therefore, the correct answer is not provided in the answer choices given.