How much should be invested now at 7.55% compounded annually to have $46,000 in 12 years?
46000=P(1.0755)^12
take the ln of each side
ln46000=ln P+12ln(1.0755)
lnP=ln(46000)-12ln(1.0755)
using the google calculator in the google search window:
ln(46000)-12ln(1.0755)=9.86296864
than taking the antilog,
P=e^9.86296864=19206 about
Po = 46,000/(1.0755^12) = $19,205.82 = Amt. invested now.
To determine how much should be invested now at 7.55% compounded annually to have $46,000 in 12 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future amount we want to have ($46,000),
P is the principal amount (the amount we need to invest now),
r is the annual interest rate (7.55% expressed as a decimal, which is 0.0755),
n is the number of compounding periods per year (since it's compounded annually, n = 1),
and t is the number of years (12).
Rearranging the formula to solve for P, we have:
P = A / (1 + r/n)^(nt)
Substituting the given values into the formula, we get:
P = $46,000 / (1 + 0.0755/1)^(1*12)
Calculating this expression, we have:
P = $46,000 / (1 + 0.0755)^12
P = $46,000 / (1.0755)^12
P ≈ $20,066.93
Therefore, approximately $20,066.93 should be invested now at a 7.55% annual interest rate compounded annually to have $46,000 in 12 years.