Question

A student has money in three accounts that pay 5%, 7%, and 8%, in annual simple (i.e. compounded once per year) interest. She has three times as much invested at 8% as she does at 5%. If the total amount she has invested is $1600 and her interest for the year comes to $115, how much money does she have in each account

Answer 1

Answer:

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $400

Amount invested in account with 8% annual interest = $900

Step-by-step explanation:

Let the money invested in account with 5% annual interest = $x$

As per question statement,

Money invested in account with 8% annual interest = $3x$

Given that total amount invested in three accounts = $1600

So, Money invested in account with 7% annual interest = 1600- $3x$ -$x$ = 1600- $4x$

For one year, the compound interest is same as that of Simple Interest.

Formula for simple interest is given as:

$SI =\dfrac{PRT}{100}$

Where, P is the amount invested

R is the annual rate of interest

T is the time for which the amount is invested.

As per question statement:

$\dfrac{x\times 5\times 1}{100}+\dfrac{(1600-4x)\times 7\times 1}{100}+\dfrac{3x\times 8\times 1}{100} =115\\\Rightarrow 5x\times +1600\times 7-28x+24x=11500\\\Rightarrow 29x-28x = 11500-11200\\\Rightarrow \bold{x =\ 300}$

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $1600-$1200 = $400

Amount invested in account with 8% annual interest = $900