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Heather has a total of
$5000 to invest. She puts part of it in an account paying
5%// year interest and the rest in a GIC paying
7.2% interest. If she has
$349 in simple interest at the end of the year, how much was invested at each rate?

$1$ . Heather has a total of $\$ 5000$ to invest. She puts part of it in an account paying $5 \% /$ year interest and the rest in a GIC paying $7.2 \%$ interest. If she has $\$ 349$ in simple interest at the end of the year, how much was invested at each rate?

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Finance problems

Full solution

Q.

1

. Heather has a total of

\$ 5000

to invest. She puts part of it in an account paying

5 \% /

year interest and the rest in a GIC paying

7.2 \%

interest. If she has

\$ 349

in simple interest at the end of the year, how much was invested at each rate?

Define variables: Step $1$ : Define the variables. $\newline$ Let $x$ be the amount invested at $5\%$ interest, and $y$ be the amount invested at $7.2\%$ interest. $\newline$ We know the total investment is $\$5000$ . $\newline$ $x + y = 5000$
Set up equation: Step $2$ : Set up the equation for the total interest earned. $\newline$ Interest from $x$ at $5\%$ plus interest from $y$ at $7.2\%$ equals $\$349$ . $\newline$ $0.05x + 0.072y = 349$
Solve system of equations: Step $3$ : Solve the system of equations. $\newline$ From Step $1$ , $y = 5000 - x$ . $\newline$ Substitute $y$ in the interest equation: $\newline$ $0.05x + 0.072(5000 - x) = 349$ $\newline$ $0.05x + 360 - 0.072x = 349$ $\newline$ $-0.022x + 360 = 349$ $\newline$ $-0.022x = -11$ $\newline$ $x = \(500\)

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