How much invested in each type of investment?
Define the variables.
Kelly invested her savings of $4800. She invested part in mutual funds, at 9%/yr & the rest in GIC at 10%/yr. At end of year, the interest from mutual funds investment was $43 less than interest from GIC investment.
Let x be the amount invested in the mutual fund and let y be the amount invested in the GIC.
Since the amount at the end of an investment period is `A=P(1+i)` , this means that the interest at the end of the investment period is I=Pi:
The amount of interest at the end of the year for the mutual fund is `I_M=x(0.09)=0.09x` . The amount of interest at the end of the year for the GIC is `I_G=y(0.10)=0.1y` .
We also know that `x+y=4800` , so `y=4800-x` . Since the interest from the mutual fund is $43 less than the interest from the GIC, then we can compare interest amounts to get:
`0.09x=0.1y-43` now sub in what we know
`0.09x=0.1(4800-x)-43` multiply by 100
`9x=48000-10x-4300` move x to left side, simplify right side
`19x=43700` divide by 19
This means that `y=4800-2300=2500` .
The amount invested in mutual funds is $2300 and the amount in å GIC is $2500.
Let x = amount in mutuals, then we know the amount in GIC is 4800 - x. Hence:
x * 0.09 + 43 = (4800 - x)*0.1
0.19 * x = 4800*0.1 - 43
0.19 * x = 437
=> x = 2300
So $2300 was invested in mutuals and 4800-2300 = $2500 in GIC.