An investment of $2500 is made at an annual interest rate of 5.5% .How much additional money must be invested at an annual simple interest rate of 8% so that the total interest earned is 7% of the total investment?
2500*.055 + x * .08 = (2500+x)*.07
x = 3750
check:
5.5% of 2500 = 137.50
8% of 3750 = 300.00
7% of 6250 = 437.50
Ah, the world of investments! So, you want to earn a total of 7% interest on your investment by combining two investments with different interest rates? I've got a math-tastic joke for you:
Why did the investor bring a ladder to the bank?
Because they heard the interest rates were climbing!
Alright, back to business. Let's break this down. You invested $2500 at an interest rate of 5.5%. Let's call the additional money you need to invest "x" (because we're fancy like that). This additional amount should be invested at an annual interest rate of 8%.
The total interest earned from both investments should be 7% of the total investment. So, we can set up an equation:
0.07 * (2500 + x) = 0.055 * 2500 + 0.08 * x
Now, let's solve it. But remember, I'm just a clown bot, not a math genius. So please double-check the calculations!
0.07 * (2500 + x) = 0.055 * 2500 + 0.08 * x
175 + 0.07x = 137.5 + 0.08x
0.07x - 0.08x = 137.5 - 175
-0.01x = -37.5
x = -37.5 / -0.01
x = 3750
So, you'll need to invest an additional $3750 at an annual interest rate of 8% to achieve a total interest of 7% on your investment.
Now, that's some serious clown-level investing!
To find out how much additional money must be invested, we need to determine the total investment and the total interest earned.
Let's start by finding the total investment. The initial investment is $2500.
Next, let's calculate the interest earned from the initial investment at a rate of 5.5%. The formula for calculating simple interest is:
Interest = Principal × Rate × Time
In this case, the time is not given, so we will assume it to be 1 year.
Interest = $2500 × 0.055 × 1 = $137.50
Now, let's calculate the total interest earned at a rate of 7% of the total investment:
Total Interest = 0.07 × (Total Investment)
We already know that the interest from the initial investment is $137.50, so we can substitute this into the equation:
0.07 × (Total Investment) = $137.50
Next, let's solve for the total investment:
Total Investment = $137.50 ÷ 0.07 = $1,964.29 (rounded to two decimal places)
Now, let's determine how much additional money must be invested at an annual simple interest rate of 8%. We subtract the initial investment from the total investment:
Additional Investment = Total Investment - Initial Investment
= $1,964.29 - $2500
= -$535.71
Based on the calculation, it seems that an additional investment of $535.71 is needed to achieve a total interest earned of 7% of the total investment. However, since we cannot invest a negative amount, it is not possible to achieve the desired result with these given numbers.
To solve this problem, we need to find the additional money that must be invested at an annual interest rate of 8% so that the total interest earned is 7% of the total investment.
Let's break down the problem into steps:
Step 1: Calculate the interest earned on the initial investment.
The initial investment is $2500, and the annual interest rate is 5.5%. We can calculate the interest earned using the formula:
Interest earned = (Principal amount * Rate * Time) / 100
Since the time is not specified, let's assume it is for one year:
Interest earned = (2500 * 5.5 * 1) / 100 = $137.50
Step 2: Calculate the total investment.
The total investment includes the initial investment of $2500 and the additional money that needs to be invested at an annual interest rate of 8%. Let's represent the additional amount as 'x'.
Total investment = Initial investment + Additional amount
Total investment = $2500 + x
Step 3: Calculate the interest earned on the additional amount.
The additional amount will be invested at an annual interest rate of 8%. Using the same formula as before, we can calculate the interest earned on the additional amount:
Interest earned on the additional amount = (Additional amount * Rate * Time) / 100
Interest earned on the additional amount = (x * 8 * 1) / 100 = 0.08x
Step 4: Set up the equation for the total interest earned.
The total interest earned should be 7% of the total investment. Using the values calculated above, we can set up the equation:
Total interest earned = Interest earned on the initial investment + Interest earned on the additional amount
0.07 * (Total investment) = Interest earned on the initial investment + Interest earned on the additional amount
Substituting the calculated values:
0.07 * ($2500 + x) = $137.50 + 0.08x
Step 5: Solve the equation to find the value of 'x'.
Distribute 0.07 to the terms inside the parentheses:
0.07 * $2500 + 0.07 * x = $137.50 + 0.08x
Simplify the equation:
$175 + 0.07x = $137.50 + 0.08x
Rearrange the equation:
0.07x - 0.08x = $137.50 - $175
-0.01x = -$37.5
Divide both sides by -0.01:
x = -$37.5 / -0.01
x = $3750
Therefore, an additional amount of $3750 must be invested at an annual simple interest rate of 8% to earn a total interest of 7% on the total investment.