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Answer :
Susie Q needs to calculate the original amount invested in the Pretty Penny bank using the known total amount after two years and the respective interest rates that compounded annually. By forming an equation that takes into account both investments and their compound growth, we can solve for the amount invested in the Pretty Penny bank.
Susie Q has \\$1000 to invest and does so in two different banks, one compounding annually at 3% and the other at 5%. After two years, the total amount she has is \\$1090.02. We need to find out how much was invested in the Pretty Penny bank with a 3% annual interest.
Let's denote the amount invested in the Pretty Penny bank as x dollars. Consequently, the remaining amount, \\$1000 - x, was invested in the Five and Dime bank at 5% interest.
The total amount after two years can be calculated from both investments:
Pretty Penny bank: x * \(1.03\)^2
Five and Dime bank: (\(1000 - x\)) * \(1.05\)^2
The sum of these investments after two years is equal to \\$1090.02:
\(x * 1.03^2\) + \((1000 - x) * 1.05^2\) = 1090.02
To find x, the amount invested in Pretty Penny bank, we'll solve the equation:
\(x * 1.0609\) + \((1000 - x) * 1.1025\) = 1090.02
If we apply order of operations and solve for x, we'll find out how much was originally invested in the Pretty Penny bank.
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Rewritten by : Barada
When calculating compound interest, the starting principle amount is multiplied by one along with the annual interest rate raised to the number of compound periods minus one.
She invested at Pretty Penny = x, where x is the compound interest.
Consequently, we may say that the amount invested is Five and Dime = 1000 - x.
Therefore, we have that: amount invested at each bank multiplied by the ultimate amount over the course of two years
Simplify the expression to x(1.03)2 + (1000 - x)(1.05)2 = 1090.0
1.0609x + (100 - x) (1.1025 ) = 1090.0
1.0609x + 1102.5 - 1.025x = 1090.02 combine like terms on the left
- Remove 1102.5 from each side of the equation (.0416x + 1102.5 = 1090.02)
Divide both sides by -.0416 to get a result of.0416x = -12.48.
$300 was invested at Pretty Penny in x, and
(1000 - x) = (1000 - 300) = 700 dollars were put into Five and Dime.
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