find the difference in financial gains when $3200 is invested for eight years with an interest rate of 4.5% for both simple interest in compound interest and interest interest is compounded annually
To find the difference in financial gains between simple interest and compound interest when $3200 is invested for eight years at an interest rate of 4.5% compounded annually, we can use the following formulas:
1. Simple Interest:
Simple Interest = (Principal) x (Interest Rate) x (Time)
Simple Interest = $3200 x 4.5% x 8 = $1152
2. Compound Interest:
Compound Interest = Principal x (1 + (Interest Rate / n))^(n x Time) - Principal
Here, n represents the number of times the interest is compounded in one year.
Since the interest is compounded annually, we can substitute n = 1 into the formula:
Compound Interest = $3200 x (1 + (4.5% / 1))^(1 x 8) - $3200
Compound Interest = $3200 x (1 + 0.045)^8 - $3200
Compound Interest = $3200 x (1.045)^8 - $3200
Compound Interest ≈ $445.35
The difference in financial gains between simple and compound interest is:
Difference = Compound Interest - Simple Interest
Difference ≈ $445.35 - $1152
Difference ≈ -$706.65
Therefore, the difference in financial gains between simple interest and compound interest when $3200 is invested for eight years at an interest rate of 4.5% compounded annually is approximately -$706.65.