find interest question

Question

Find the present value of $3,000.00 if interest is 6% compounded quarterly for 5 years

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use here for compound interest is

PV = FV / (1 + r/n)^(nt)

In this scenario we’re plugging in FV = 3000, r = 0.06, n = 4, and t = 5 in order to get

PV = 3000 / (1 + 0.06/4)^(4*5) = 2227.41

Meaning that the present value here after the 5 years is going to be $2,227.41

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

I think you need to reword your question.  The way it is stated the answer is 3000.  This could be on purpose, but i doubt it.  I'm guessing its the way steve did it since the question does say present value and he is assuming the 3000 is future.  Right now, its ambiguous.

Answer 3

A = P (1 + r/n)^(nt)

 

Since we're asked to find the "present value", the $3000 must be the "future value" in 5 years. I.e., A = $3000, P = "present value", r = 0.06, n = 4, t = 5.

 

Substitute into the formula:

3000 = P (1 + 0.06/4)^(4*5)

 

Solve for P:

P = (3000)/((1.015)^20) ≈ $2,227.41

 

Calculators may behave differently, but here are the keystrokes on the Mac OS X calculator in Scientific mode:

3000 [÷] 1.015 [y^x] 20 [=]

Answer 4

3,000 * (1 + .06/4)^5*4

 

3,000 * (1.015)²⁰

 

3,000 / 1.347 = $2,227.17