A company invested $29,000, putting part of it into a savings account that earned 3.2% annual simple interest and the remainder in a stock fund that earned 12.4% annual simple interest. If the investments earned $1572 annually, how much was in each account?

Question

photon336 · Answer

Do you know the simple interest formula?

candycanegone · Answer

No :/

photon336 · Answer

Interest = principle*rate*time

candycanegone · Answer

oh how would i set it up?? lost about that

photon336 · Answer

$$I = P_{0}*r_{1}*t_{1}$$

$$I_{2} = P_{2}*r_{2}*t_{2}$$


annually means 1 year so t2 = t1 which is just 1 

$$I_{1} = P_{0}(r_{1})$$

$$I_{2} = P_{1}(r_{2})$$

we know that the initial values invested are different  P0 in one account and P1 in the other but their sums are 

$$P_{0}+P_{1} = (29,000)$$ 

and  we know that the sum of the interest is 1,572. that includes the two here. 

$$P_{1}r_{2}+P_{0}r_{1} = $1,572$$ 

because we've got two different variables we need to equations.

candycanegone · Answer

ok how do i solve for that ti looks confusing :(

photon336 · Answer

alright so 

we know that the sum of the deposits of both accounts must equal 29,000 right?

photon336 · Answer

@candycanegone

photon336 · Answer

Like we know that we deposited two different amounts into two separate investment accounts. 

well call those P0 and P1

photon336 · Answer

Here are the two equations you must solve. 

$$P_{0}+P_{1} = 29,000$$ 

$$P_{0}(0.032)+P_{1}(0.12) = 1,572$$

photon336 · Answer

The second equation is just the simple interest formula. note I took the decimal form of both percentages. now the key here, is to add these up because 

Interest = P*r*t 

so the total interest earned would be 

P*r*t1 + P*r*t1 

since t is just a year we can just disregard it and now it becomes: 

$$P_{0}(0.032)+P_{1}(0.124) = 1,574$$

$$p_{0}+p_{1} = 29,000$$

$$P_{0} = 29,000-P_{1}$$

Substitute this into the first equation. 

$$(29,000)*(0.032)-(P_{1})0.032+P_{1}(0.124) = 1,572$$

We clean this up a bit 

$$928+0.092P_{1} = $1,572$$ 

$$P_{1} =\frac{ 644 }{ 0.092 } = $7,000$$ 

so one account 7,000 was placed into it. 

can you find the amount of money placed into the other account? it's more straight forward.