Question

If $10900 is invested at an annual interest rate of 6%, find the value of the investment at the end of 9 years for the following compounding methods.
PLEASE IF THERE IS A WAY TO INPUT THIS INTO DESMOS PLEASE EXPLAIN HOW ALSO..THANK YOU!

Answer 1

The formula to use is

A = P*(1+r/n)^(n*t)

where P, r and t are fixed values given as such

• P = 10900
• r = 0.06
• t = 9

Note how I'm using the decimal form of 6%. If we let n vary, then we're basically making this the x value. So replace n with x. Let A = f(x)

Doing all these substitutions has

A = P*(1+r/n)^(n*t)

transform into

f(x) = 10900*(1+0.06/x)^(x*9)

which can be typed into desmos as you can see in the attached screenshot image below

Then on the next line, you can input f(1) to find the y output value when x = 1. This is the same as finding the value of A when n = 1. In other words, this finds out how much money you get after compounding annually (or 1 time per year). Repeat for...

• f(2) for semiannually compounding
• f(4) for quarterly compounding
• f(12) for monthly compounding
• f(52) for weekly compounding
• f(365) for daily compounding

The continuous compounding will need another formula. That formula is

A = P*e^(r*t)

The A, P, r and t are the same from before. The new addition is the 'e'. This is a special constant much like pi = 3.14 is. In this case, e = 2.718 approximately. This number 'e' shows up in a lot of math problems.