Problema Solution
Determine the principal P that must be invested at rate r = 9%, compounded monthly, so that $500,000 will be available for retirement in t = 9 years. (Round your answer to the nearest cent.)
Answer provided by our tutors
Let
P = the principal invested
r = 0.09 or 9% annual interest rate
t = 9 years
n = 12*t = 12*9 = 108 compounding periods (the account is compounded monthly)
A = $500,000 future value
A = P(1 + r/12)^n
500000 = P(1 + 0.09/12)^108
P(1 + 0.09/12)^108 = 500000
P*1.0075^109 = 500000
........
........
P = $221,441.51
The principal that must be invested is $221,441.51.