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)
$198.72
$1,350.72
$47,810.80
$231.57
To find the difference in financial gains between simple interest and compound interest, we can use the formula:
Simple Interest = P(1 + rt)
Compound Interest = P(1 + r)^t
Where:
P = Principal amount (initial investment)
r = Interest rate
t = Time period in years
For simple interest:
Principal (P) = $3,200
Interest rate (r) = 4.5% = 0.045
Time period (t) = 8 years
Simple Interest = 3200(1 + 0.045*8)
Simple Interest = $3200(1 + 0.36)
Simple Interest = $3200(1.36)
Simple Interest = $4352
For compound interest, we use the same values except that the formula includes an exponent for the time period:
Principal (P) = $3,200
Interest rate (r) = 4.5% = 0.045
Time period (t) = 8 years
Compound Interest = 3200(1 + 0.045)^8
Compound Interest = $3200(1 + 0.0416)^8
Compound Interest = $3200(1.0416)^8
Compound Interest = $3200(1.3639)
Compound Interest = $4364.48
The difference in financial gains is:
Difference = Compound Interest - Simple Interest
Difference = $4364.48 - $4352
Difference = $12.48
Therefore, 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 is approximately $12.48.