i need help on an investment problem.
equal amounts are invested at 6%, 7%, and 8% anual interest. If the three investments yield a total of $2037 annual interest, find the total investment?
+128732 I'm assuming that the investment is for one year......remember that: I = Pr where I is the interest earned, P is the principal, and r is the interest rate.....so we have.......
.06P + .07P + .08P = 2037 simplify
P(.21) = 2037 divide both sides by .21
P = $9700 ......so this is the equal amount invested at the different rates
+128732 I'm assuming that the investment is for one year......remember that: I = Pr where I is the interest earned, P is the principal, and r is the interest rate.....so we have.......
.06P + .07P + .08P = 2037 simplify
P(.21) = 2037 divide both sides by .21
P = $9700 ......so this is the equal amount invested at the different rates
If you take the simple average of the interest rate, then it naturally is 6+7+8=21/3=7%
Therefore, the total investment will be $2,037.00/.07=$29,100. However, the more accurate method would be to compound the interest thus:1.06 x 1.07 x 1.08=1.224936^(1/3)=6.996884644.
Therefore the total investment would be=$2,037.00/.06996884644=$29,112.96.
As you can see, the difference is quite minor, but in the long run it would make significant impact.
