$3,000 is invested in an account paying 4% interest and twice that amount is invested at 6%. How do you write the expression that represents the amount of interest earned on the money invested at 6%?

1 Answer
Aug 1, 2018

See explanation

Explanation:

Assumption: The interest given is the ul("yearly interest rate")

Twice the amount is $6000

Let the count of years be n

color(brown)("At 6% "ul("simple")" interest calculated once per year is:")

$6000+[nxx(6/100xx$6000)]

Factoring out the $6000 giving:

$6000(1+(6n)/100)

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color(brown)("At 6% annually "ul("compounded monthly")

The 6% is 'spread' over each calculation cycle. There are 12 months in a year so instead of 6/100 we have 6/100xx1/12

Note that the count in years is n. However ther are 12 calculations cycles in one year so the 'power' of n becomes 12n instead.

$6000(1+6/(12xx100))^(12xxn)

$6000(1+cancel(6)^1/cancel(1200)^600)^(12n)

$6000(1+1/600)^(12n)