Monthly compounding word problem

Question

Jane Roznowski wants to invest some money now to buy a new tractor in the future. If  she wants to have

​$325,000 available in 6 years, how much does she need to invest now in a CD paying

4.85% interest compounded monthly?

I already have the formula and have seen examples with other numbers but cannot understand how they got the answer..... I just need the answer so I can turn in my homework and be done with this class HELP!!

Answer 1

Let's let P be our initial Principal.

After 1 month, our compound period, P has accrued interest. Your balance is now P*(1 + .0485/12).

After another month, Your balance would be (P*(1+.0485/12))*(1+.0485).

Simplifying, this would be, after 2 months, P*(1+.0485/12)^2

After 3 months, P*(1+.0485/12)^3

After 4 months, P*(1+.0485/12)^4

If it does this for 6 years, or 72 months, then it will be P(1+.0485/12)^72. We set this equal to $325,000 and solve for P:

P = ($325000)/((1+.0485/12)^72)

P = $243085.19