Question

PLEASE HELP!!
nico is saving money for his college education. he invests some money at 6% and $1900 less than the amount at 5%. the investments produced a total of $191 interest in 1 yr. how much did he invest at each rate?

Answer 1

PLEASE HELP ME

Answer 2

Is the interest simple of compounding? That'll be key to calculating this one.

If it is compound, what is the compounding frequency?

Answer 3

thats whats confusing me. i dont know how to do this

Answer 4

Let's look at the simple interest case. It is more approachable.

Answer 5

okay

Answer 6

its asking for the interest at each rate
5% and 6%

Answer 7

i gave up on this problem so i didnt know what to do @eashmore

Answer 8

Simple interest always pays interest against the original amount invested.

Let's say I invested $100 with a bank with a simple interest rate of 5% a year.
At the end of the first year, I would have $105 in the bank. That's because 5% of 100 is 5, so they pay me $5.

The formula to calculate interest paid on a load (or paid to a savings account) is\[I = P * R * T\]
I is the interest paid. In my example about, that is $5.
P is the principle (or original amount borrowed or saved). In my example is $100.
R is the interest rate (expressed as a decimal). In my example is 5%.
T is the time. We want to use the same unit of time as the interest is paid. In my example, we get paid interest every year.

The question gives us the Interest (I) earned. We can assume interest is paid our annually so Time (T) will be 1. It also gives us some idea about how much was invested at different interest rates. If x is the amount we invested, we will have two equations. I_1 is amount of interest earned at 6% and I_2 is the amount of interest earned at 5%.

\[I_1 = x * 0.06 * 1\]\[I_2 = (x-1900)*0.05*1\]
Together, these add to $191.
So we get\[I_1 + I_2 = 191\]We need to substitute in our equations\[x * 0.06 * 1 - (x-1900) * 0.05 * 1 = 191\]

Answer 9

My last equation has a typo. It should be a plus\[x*0.06*1 + (x-1900) * 0.05 *1 = 191\]

Answer 10

Now we can combine like terms. \[0.06x + 0.05x - (1900*0.05) = 191\]\[0.11x - (1900*0.05) = 191\]

Answer 11

If we solve for x we determine how much was invested at 6%.
The amount invested at 5% will be x - 1900.

Answer 12

i dont know how to solve for x to get the amount invested at 6% im stumped there

Answer 13

@eashmore

Answer 14

Take 1900*.05. What do you get?

Answer 15

950

Answer 16

is that for 6% or 5%

Answer 17

We have to solve the equation.

\[0.11x - (1900*0.05) = 191\]

Answer 18

THe first step is to find the product within the parenthesis. This is 1900 times 0.05.

Answer 19

You should get 95.

Answer 20

Now, we have \[0.11x - 95 = 191\]

Answer 21

We need to add 95 to both sides.

Answer 22

Now we have \[0.11x = 286\]

Answer 23

Divide by 0.11\[x = 2600\]

Answer 24

X is amount invested at 6%.

In my earlier expression, we defined what was invested at 5% to relate to what was invested at 6% as (x-1900)

Answer 25

is the 2600 for 5% or 6%

Answer 26

This helps us get down to one variable to solve for.

Answer 27

so the 2600 is for six percent???

Answer 28

The problem states that some amount is invested at 6%. We will call this x.
The problem states that he invests 1900 less than this amount at 5%. Therefore, the amount invested at 5% is equal to x-1900.
We are relating the two investment amounts as given in the problem statement.

Answer 29

We solved the equation and determined that x was 2600. Which is the amount invested at 6%.

What is the amount invested at 5% if it is 1900 less than the amount invested at 6%?

Answer 30

subsitute x for 2600 and then subtract 2600-1900???

Answer 31

if so then 700 is what i get but plz let me know if thats right

Answer 32

@eashmore am i right if 2600-1900 is what i have to do then i get 700
is that right that he invested 700 at 5%??

Answer 33

Correct.