Question

You received an inheritance of $40,000 from a beloved uncle. With inflation so high, you decided that rather than save the inheritance, you are going to invest it. You were given two interest bearing accounts to invest in. One yields 7% simple interest and other pays 6.5%. You expect earn $2,640 in interest in total from both accounts in the first year. How much should you invest in each account?

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Let's denote the amount invested in the account yielding 7% simple interest as \(x\) dollars and the amount invested in the account yielding 6.5% simple interest as \(40000 - x\) dollars (since the total inheritance is $40,000).
The interest earned from the first account (\(7\%\) interest rate) is \(0.07x\) dollars.
The interest earned from the second account (\(6.5\%\) interest rate) is \(0.065(40000 - x)\) dollars.
We know that the total interest earned from both accounts is $2,640.
So, we can write the equation:
\[ 0.07x + 0.065(40000 - x) = 2640 \]
Let's solve for \(x\) :
\[ 0.07x + 0.065(40000 - x) = 2640 \]
\[ 0.07x + 2600 - 0.065x = 2640 \]
\[ 0.005x = 40 \]
\[ x = \frac{40}{0.005} \]
\[ x = 8000 \]
So, you should invest $8,000 in the account yielding 7% simple interest, and the remaining amount, $32,000, in the account yielding 6.5% simple interest.

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