Interest Word Problem

Question

You win $24,000 and you decide to invest the money in two different investments: one paying 18% and the other paying 12%. A year later you have $27,480 total. How much did you originally invest in each account?

Answer 1

Since the question does not says if the interest rates are simple and yearly or complex and yearly or quarterly, but the yield is obtained after one year, I am assuming the rate of interests are simple and yearly.

Lets, $x from $24,000 was invested @ 18%

hence, ($24,000-$x) was invested @ 12%

thus, $x @ 18% simple rate of yearly interest becomes =$(118x/100)

and ($24,000-$x) @ 12% simple rate of yearly interest becomes = [112($24,000-$x)/100]=$[26880-(112x/100)]

therefore,

(118x/100)+26880-(112x/100)=27480

=>(118x/100)-(112x/100)=600 ...... subtracting 26880 from both sides

=>118x-112x=60000 ........................multiplying both sides by 100

=>6x=60000...................simplifying

=>x=10000.................dividing both sides by 6

therefore, $10,000 was invested at 18% simple rate of yearly interest and $14,000 was invested at 12% simple rate of yearly interest.