<PRE><B>Question 1132304</B>
what i get is as follows.


if the percent interest rate is m, then the interest rate is m / 100.


if the percent interest rate is n, then the interest rate is n / 100.


i = p * r * t.


t = 1 because we&#39;re dealing with 1 year only.


that makes i = p * r.


for the m percent rate, the formula becomes i1 = p * m / 100


for the n percent rate, the formula becomes i2 = p * 2 * n / 100


d is the total interest and is therefore equal to i1 + i2 which makes it equal to p * m / 100 + p * 2 * n / 100.


since the denominator is the same, the formula becomes d = (p * m + p * 2 * n) / 100


you can factor out the p to get d = p * (m + 2 * n) / 100


if you solve for p, you get p = 100 * d / (m + 2 * n)


the total amount loaned would be p + 2 * p = 3 * p


since p = 100 * d / (m + 2 * n), then 3 * p = 3 * 100 * d / (m + 2 * n).


that makes 3 * p = 300 * d / (m + 2 * n).


how do you know this formula is good?


you need to put in some randomly generated numbers and see if they come out as you would expect.


i chose p = 1000 and m = 10% and n = 20%.


per the formula of d = p * (m + 2 * n) / 100, you get:


d = 1000 * (10 + 2 * 20) / 100 = 1000 * 50 / 100 = 1000 * .5 = 500


d = 500 = total interest from both investments.


the total amount loaned should be equal to p + 2 * p = 3 * p = 3000.


given d = 500 and m = 10% and n = 20%, and given the formula of 3 * p = 300 * d / (m + 2 * n), you get:


3 * p = 300 * d / (m + 2 * n) becomes 3 * p = 300 * 500 / (10 + 2 * 20) which becomes 3 * p = 150000 / 50 which becomes 3 * p = 3000.


that checks out ok, so the solution looks good.


the formulas check out with the logic.


your solution is that the total amount loaned is equal to 3 * p which is equal to 300 * d / (m + 2 * n).


if you know d and m and n, you can find 3 * p per the formula.


3 * p is the total amount loaned.


if t is not equal to 1, then it becomes patt of the equation.


the interest per year will be the same because you are dealing with simple interest which is calculated off the initial investment only.


instead of i = p * r, you get i = p * r * t.


let me know if you have any questions regarding this.











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