SOLUTION: find the time taken for a certain sum of money to double if the interest rate is 12% per annum compounded semi-annually

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: find the time taken for a certain sum of money to double if the interest rate is 12% per annum compounded semi-annually      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1087828: find the time taken for a certain sum of money to double if the interest rate is 12% per annum compounded semi-annually
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find the time taken for a certain sum of money to double if the interest rate is 12% per annum compounded semi-annually
:
let the original amt = 1,
then
the final amt = 2
:
Compound interest formula
A+=+p%281+%2B+r%2Fn%29%5E%28nt%29,where:
A = Final amt (2)
P = Initial amt (1)
r = interest rate in decimal form (.12)
n = Compounding times per year (2)
t = no. of yrs
:
2 = 1%281+%2B+.12%2F2%29%5E%282t%29,
1.06%5E%282t%29%29+=+2
Use nat logs
ln%281.06%5E%282t%29%29+=+ln%282%29
log equiv of exponents
2t%2Aln%281.06%29+=+ln%282%29
2t = ln%282%29%2Fln%281.06%29
use your calc
2t = 11.9
t = 11.9/2
t = 5.95 ~ 6 yrs