Need help find P in a compound interest question.

Question

Determine the principal P that must be invested at rate r = 4%, compounded monthly, so that $500,000 will be available for retirement in t = 10 years.

 

P= $?

Answer 1

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

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

solving that for the variable "P" yields

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

for this scenario that means taking

P = 500000 / (1 + 0.04/12)^(12*10)

P = 335,383.04

meaning that to have $500,000 available for retirement in 10 years, you would need to invest a principal of $335,383.04 today

Answer 2

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

 

500000 = P(1 + 0.04/12)^(12)(10)

500000 = P(1.0033)¹²⁰

500000 = P(1.49)

335383.04 = P