SOLUTION: Q: The simple interest on a certain principal for 9 months at 4% rate is 150$ less than the interest on the same principal for 16 months at 6% rate.What is the principal? Sol pl

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Q: The simple interest on a certain principal for 9 months at 4% rate is 150$ less than the interest on the same principal for 16 months at 6% rate.What is the principal? Sol pl      Log On

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Question 1032329: Q: The simple interest on a certain principal for 9 months at 4% rate is 150$ less than the interest on the same principal for 16 months at 6% rate.What is the principal?
Sol please!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
simple interest = p * r * n

p is the principal
i is the interest rate per year.
n is the number of years.

4% interest per year for 9 months would be equal to p * .04 * 9/12 years.

6% interest per year for 16 months would be equal to p * .06 * 16/12 years.

you are given that the 4% interest for 9 months is 150 dollars less than the 6% interest for 16 months.

your equation is:

p * .04 * 9/12 = p * .06 * 16/12 - 150

simplify to get .03 * p = .08 * p - 150

add 150 to both sides of the equation and subtract .03 * p from both sides of the equation to get:

150 = .08 * p - .03 * p

simplify to get 150 = .05 * p

divide both sides of the equation by .05 to get 150 / .05 = p.

simplify to get 3000 = p

your principal is 3000.

.04 * 3000 * 9/12 = 90 dollars

.06 * 3000 * 16/12 = 240 dollars

240 - 90 = 150

solution looks good.

the interest on the 4% loan for 9 months is 150 dollars less than the interest on the 6% loan for 16 months.