Problem:
Geoff has $5000 to invest. He wants to earn $568 in interest in one year. He will invest part of the money at 12% and the other part at 10%. How will he invest.
+I already know how to do Simplest Interest, I just can't read the problem to find what
i =
p =
r =
t =
(5000 - x).12 + x(.10) = 568
(5000).12 - (x).12 + x(.10) = 568
600 - .12x + .1x = 568
subtract 600 from both sides
-.12x + .1x = -32
-.02x = -32
divide both sides by -.02
x = 1600
3400 at 12% and 1600 at 10%
a loan of 25,000 its due in 9 months with an annual interest rate of 10%. Find the total amount that will be due.
To find out how Geoff will invest his money, we need to determine the amount he will invest at each interest rate.
Let's assume the amount Geoff will invest at 12% interest rate is x dollars. Therefore, the amount he will invest at 10% interest rate is ($5000 - x) dollars (since he has a total of $5000 to invest).
To calculate the interest earned at 12%, we will use the formula for simple interest:
i = p * r * t
Where:
i = interest earned,
p = principal (the amount invested),
r = rate of interest, and
t = time in years.
Given that Geoff wants to earn $568 in interest in one year, we can set up the equation:
568 = x * 0.12 * 1
Simplifying the equation, we get:
568 = 0.12x
Next, let's find the amount he will invest at 10% interest rate:
Amount invested at 10% = $5000 - x
To solve for x, we can substitute this value into the equation we obtained earlier:
568 = 0.12x
x = 568 / 0.12
x ≈ $4733.33
This means Geoff will invest approximately $4733.33 at a 12% interest rate. Therefore, he will invest the remaining amount, ($5000 - $4733.33) = $266.67 at a 10% interest rate.
To summarize, Geoff will invest approximately $4733.33 at a 12% interest rate and $266.67 at a 10% interest rate.