SOLUTION: [A=P(1+r/n)^nt] Amount invested: $12,500 No. of compounding periods:4 Annual interest rate: 5.75% Accumulated amount: $20,000 Time t in years?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: [A=P(1+r/n)^nt] Amount invested: $12,500 No. of compounding periods:4 Annual interest rate: 5.75% Accumulated amount: $20,000 Time t in years?      Log On


   

Question 471320: [A=P(1+r/n)^nt]
Amount invested: $12,500
No. of compounding periods:4
Annual interest rate: 5.75%
Accumulated amount: $20,000
Time t in years?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


20000=12500%281%2B0.0575%2F4%29%5E%284%2At%29 Plug in A=20000, P=12500, r=0.0575 (the decimal equivalent of 5.75%), and n=4.


20000=12500%281%2B0.014375%29%5E%284%2At%29 Evaluate 0.0575%2F4 to get 0.014375


20000=12500%281.014375%29%5E%284%2At%29 Add 1 to 0.014375 to get 1.014375


20000%2F12500=%281.014375%29%5E%284%2At%29 Divide both sides by 12500.


1.6=%281.014375%29%5E%284%2At%29 Evaluate 20000%2F12500 to get 1.6.


ln%281.6%29=ln%28%281.014375%29%5E%284%2At%29%29 Take the natural log of both sides.


ln%281.6%29=4%2At%2Aln%281.014375%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


ln%281.6%29%2Fln%281.014375%29=4%2At Divide both sides by ln%281.014375%29.


0.470003629245736%2Fln%281.014375%29=4%2At Evaluate the natural log of 1.6 to get 0.470003629245736.


0.470003629245736%2F0.0142726592867186=4%2At Evaluate the natural log of 1.014375 to get 0.0142726592867186.


32.930347442897=4%2At Divide.


32.930347442897%2F4=t Divide both sides by 4 to isolate "t".


8.23258686072426=t Divide.


t=8.23258686072426 Rearrange the equation.


So it will take about 8.23 years