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.
To find the difference in financial gains, we need to calculate the amount of money earned from both simple interest and compound interest.
For simple interest, we use the formula:
Simple Interest = Principal × Rate × Time
Simple Interest = $3,200 × 0.045 × 8
Simple Interest = $1,152
For compound interest, we use the formula:
Compound Interest = Principal × (1 + Rate)^Time - Principal
Compound Interest = $3,200 × (1 + 0.045)^8 - $3,200
Compound Interest = $3,200 × (1.045)^8 - $3,200
Compound Interest ≈ $3,200 × 1.388641 - $3,200
Compound Interest ≈ $4,443.65 - $3,200
Compound Interest ≈ $1,243.65
The difference in financial gains is the compound interest earned minus the simple interest earned:
Difference = Compound Interest - Simple Interest
Difference = $1,243.65 - $1,152
Difference ≈ $91.65
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 $91.65.