An investment of $3,000 is made at an annual simple interest of 5%. How much additional monery must be invested at an annual simple interest rate of 8% so that the total annual interest earned is 7.5 of te original amount that you invested?
Me too bro. Good luck
$2400 at 7% for one and a half years.
To find out how much additional money needs to be invested at a different interest rate, we need to follow these steps:
Step 1: Find the interest earned on the initial investment.
The formula to calculate the interest earned is:
Interest = Principal * Rate * Time
Given:
Principal (P) = $3,000
Rate (R) = 5% = 0.05 (decimal)
Time (T) = 1 year
Substituting the values into the formula, we get:
Interest = $3,000 * 0.05 * 1 = $150
Step 2: Determine the total interest that needs to be earned.
The question states that the total annual interest earned should be 7.5 times the original amount invested.
Total Interest = 7.5 * Initial Investment
Total Interest = 7.5 * $3,000
Total Interest = $22,500
Step 3: Calculate the additional amount needed to reach the total interest.
Let's assume the additional amount to be invested is X.
The interest earned from this additional amount at an annual interest rate of 8% would be:
Interest = X * 0.08 * 1 = 0.08X
To meet the conditions stated in the question, the total interest earned must be $22,500. Therefore, we can write the equation:
$150 + 0.08X = $22,500
Step 4: Solve the equation to find the value of X.
Subtract $150 from both sides of the equation:
0.08X = $22,500 - $150
0.08X = $22,350
Divide both sides of the equation by 0.08:
X = $22,350 / 0.08
X = $279,375
Therefore, an additional amount of $279,375 needs to be invested at an annual simple interest rate of 8% to earn a total annual interest of 7.5 times the original investment of $3,000.