Larry Mitchell invested part of his $17000 advance at 2% annual simple interest and the rest at 5% annual simple interest. If his total yearly interest from both accounts was $610, find the amount invested at each rate

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AdreyE19322 AdreyE19322

25-10-2022
Mathematics

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Larry Mitchell invested part of his $17000 advance at 2% annual simple interest and the rest at 5% annual simple interest. If his total yearly interest from both accounts was $610, find the amount invested at each rate

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SanjayM661842 SanjayM661842 · Answer 1 · 2022-10-25T11:43:26+02:00

The simple interest is given by:

[tex]SI=Prt[/tex]

where P is the principal (the amount we invest in the account), r is the interest rate and t is the time of investment.

Let P be the interest Larry made in the 2% account, the simple interest in this case is given by:

[tex]0.02P[/tex]

Now for the second account we would have an envestment of (17000-P), then the simple interest have to be:

[tex]0.05(17000-P)[/tex]

and we know that both investments have to be equal to 610, then we have:

[tex]\begin{gathered} 0.02P+0.05(17000-P)=610 \\ 0.02P+850-0.05P=610 \\ -0.03P=610-850 \\ -0.03P=-240 \\ P=\frac{-240}{-0.03} \\ P=8000 \end{gathered}[/tex]

Therefore Larry invested $8000 in the 2% account and $9000 in the 5% account.