which variable within a simple interest formula influences the greatest amount of interest?

Question

this is interesting to me as i am an investor working out which variable, (the principal sum, the terms of months, and the interest rate) is the deciding factor on how to get the most interest from an investment. Any answers or suggestions would be awesome with some explanation please. :)

Answer 1

The answer is that it depends on your options. If you have a range of options, you can find which one is optimal, or for a particular interest rate, number of months, and principal investment you can compare a (25)% increase in one of the variables to a (25)% increase in another variable

Let's look at an example. The total amount of money in the account after $t$ units of time with principal investment $P$ and interest rate $r$ compounded $n$ times per year is: $A = P(1 + r/n)^{nt}$

Example: $P=40,000$, $r = .04= 4\%$, monthly compounding $n=12$ over $t=4$ years. A \$40,000 dollar investment is made for 4 years with annual interest rate of 4%. Interest is compounded monthly. \$46,927.95 is the balance after 4 years. Thus \$6,927.95 interest was earned.

If we change only the interest rate to 5%, the interest gained after 4 years is \$8,835.81. If we change only the number of years to 5, the interest gained after 5 years is \$8,839.86. If we change only the Principal to \$50,000, the interest gained after 4 years is \$8,659.93.

For the particular values I chose, a 25% increase in duration had a similar (.04% difference in interest gained) impact to a 25% increase in interest rate. Both of these had a stronger impact (about 2% difference in interest gained) than changing the principal investment by 25%.