An investment club placed $36,000 into two simple interest accounts. On one account, the annual simple interest rate is 8.5%. On the other, the annual simple interest rate is 3.5%. How much should be invested in each account so that both accounts earn the same annual interest?

Question

An investment club placed $36,000 into two simple interest accounts. On one account, the annual simple interest rate is 8.5%. On the other, the annual simple interest rate is 3.5%. How much should be invested in each account so that both accounts earn the same annual interest?

Answer 1

If x is at 8.5%, then the rest (36000-x) is at 3.5%

So, equate the interests earned:

.085x = .035(36000-x)

Answer 2

To determine the amount to be invested in each account, we can use the equation for simple interest:

Interest = Principal × Rate × Time

Let's assume that x dollars is invested in the account with an 8.5% interest rate. Hence, the remaining amount, (36000 - x), is invested in the account with a 3.5% interest rate.

For the account with an 8.5% interest rate:
Interest_1 = x × 0.085 × 1 = 0.085x

For the account with a 3.5% interest rate:
Interest_2 = (36000 - x) × 0.035 × 1 = 0.035(36000 - x)

Since both accounts should earn the same annual interest, we can set the two equations equal to each other and solve for x.

0.085x = 0.035(36000 - x)

Now, let's solve for x:

0.085x = 0.035(36000 - x)
0.085x = 1260 - 0.035x
0.085x + 0.035x = 1260
0.12x = 1260
x = 1260 / 0.12
x = 10500

Therefore, $10,500 should be invested in the account with an 8.5% interest rate, and the remainder, (36000 - 10500) = $25,500, should be invested in the account with a 3.5% interest rate.

Answer 3

To solve this problem, let's first define some variables:

Let's call the amount of money invested at 8.5% interest rate A, and the amount of money invested at 3.5% interest rate B.

Now, let's set up the equation based on the information given:

For the account with the 8.5% interest rate:
The amount of interest earned on this account can be calculated using the formula:
Interest = Principal * Rate
Interest_A = A * 8.5/100

For the account with the 3.5% interest rate:
Similarly, the amount of interest earned on this account can be calculated using the same formula:
Interest_B = B * 3.5/100

Since we want both accounts to earn the same annual interest, we can set up the following equation:
Interest_A = Interest_B

Substituting the formulas for Interest_A and Interest_B, we have:
A * 8.5/100 = B * 3.5/100

Now we can simplify the equation:
A * 8.5 = B * 3.5

We also know that the total amount invested is $36,000:
A + B = $36,000

Now we have a system of two equations:
A * 8.5 = B * 3.5
A + B = $36,000

We can solve this system of equations to find the values of A and B.