Sam Z. answered • 4d

Math/Science Tutor

Interest=fv=p(1+int/c)^(nt)

future value

premium

int%

compound

years

times/yr

Sam Z.

3d

Caleb G.

asked • 4dToday, a couple invested $92,000 ** separately** They figure that in 10 years, they will have a combined total interest of $168,132.75 . Person X has an interest rate of 10% and person Y has and interest rate of 12% compounded annually. How much did each person invest?

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Sam Z. answered • 4d

Math/Science Tutor

Interest=fv=p(1+int/c)^(nt)

future value

premium

int%

compound

years

times/yr

Sam Z.

tutor

Here's another formula: p1(1.1)^10+p2(1.12)^10-92
i got: p1=50; p2=42
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3d

Michael H. answered • 4d

High School Math, Physics, Computer Science & SAT/GRE/AP/PRAXIS Prep

Let x = the amount person X invested at 10% per year, using an assumed annual compounding.

Let y = the amount person Y invested at 12% per year, using annual compounding.

When A dollars earns interest at the rate of i per compounding interval, the investment grows in n compounding units of time to a value of F given by:

F = A*(1+i)^{n}

and the interest earned I is computed as

I = F - A = A * [ 1 - (1+i)^{n}]

Let I_{x} and I_{y} be the interest earned by X and Y. Thus

I_{x }= x * [(1+i)^{n} - 1] (where i is the growth rate of x's investment)

I_{y} = y * [(1+j)^{n} - 1] (where j is the growth rate of y's investment)

We are given the following info:

92000 = x + y

168,132.75 = I_{x} + I_{y}

Now can proceed as follows:

I_{x} = x * [ (1 + 0.10)^{10} - 1 ] = 1.5937425 x

I_{y} = y * [ (1 + 0.12)^{10} - 1 ] = 2.1058482 y

168,132.75 = I_{x} + I_{y}

y = 9200 - x

I_{y} = 2.1058482 * (92000 - x) = 193738.034 - 2.1058482 x

168,132.75 = I_{x} + I_{y} = 1.5937425 x + ( 193738.034 - 2.1058482 x )

-25605.284 = -0.5121057 x

x = 49,996,60

y = 92000 - x = 42,003.40

if the compounding assumption made above is incorrect, then at least this gives an idea of how to proceed.

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Caleb G.

thank you for your answer however, I need to know how i can apply the compound interest formula to my equation. i know that X + Y = 92,000 but im lost how to form the second equation so i can solve for my variables.3d