word prob's involving interest: How much at each rate?

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tseday871221

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i WOULD REALLY APPRECIATE IF SOMEONE COULD HELP ME SOLVE THIS PROBLEM?

Bruce invested a sum of money at 10% annual simple interest and invested twice that amount at 12% annual simple interest. If his total yearly income from both investments was $ 2890. how much was invested at each rate?

I would like to know how I would go about solving an equation like this and is there a simpler way to solve such a problem or problems like this that may entail alittle bit more information ?
 
Amount,A, after n years, equals the principal,P, times [1+i]n where i is the simple interest rate
A =P[1+i] n

let the principal be S, invested for 1 year at 10% [.10] Then
A= S[1+.1]

let 2S be invested for 1 year at 12%
A=2S[1+.12]

the total interest he received was S[1.1]+2S[1.12]
the total = 2890
S[ 1.1+2.24]=2890
S= 2890/3.34
S=$865.27 answer

Arthur
 
Re: PROBLEMS INVOLVING INTEREST

tseday871221 said:
i WOULD REALLY APPRECIATE IF SOMEONE COULD HELP ME SOLVE THIS PROBLEM?

Bruce invessted a sum of money at 10% annual simple interest and invested twice that amount at 12% annual simple interest. If his total yearly income from both investments was $ 2890. how much was invested at each rate?

I would like to know how I would go about solving an equation like this and is there a simpler way to solve such a problem or problems like this that may entail alittle bit more information ?
Click to expand...

Let x = amount invested at 10%
Then 2x = amount invested at 12%

Simple interest formula: I = P*r*t

So, when p = x, r = 10% or 0.1, and t = 1 year,
I = x*.1*1
I = .1x

And when p = 2x, r = 12% or 0.12, and t = 1 year,
I = 2x*.12*1
I = .24x

Since his total INCOME from the two investments is $2890, the total of the interest earned must be $2890:

.1x + .24x = 2890
.34x = 2890
x = 8500

So, he invested $8500 at 10%, and 2x or $17000 at 12%.

I hope this helps you.
 
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