Question 823169: How long will it take for 1000 to double, in an investment, when interest is compounded monthly at the rate of 5.8% per year? Answer by Edwin McCravy(20054) (Show Source):
$1000 will have doubled when the final amount is $2000
Use the formula:
A = P(1+)nt
where
A = the final amount = $2000
P = the beginning amount = $1000
r = the interest rate per year expressed as a decimal = 0.058
n = the number of times per year the interest is compounded = 12
t = the number of years = the unknown quantity
Substituting the known quantities
2000 = 1000(1+)12t
Divide both sides by 1000
2 = (1+)12t
Take logs of both sides:
log(2) = log(1+)12t
Use the rule of logs:
log(2) = 12t·log(1+)
Use calculator:
0.3010299957 = 12t·log(1.004833333)
0.3010299957 = 12t(0.0020940335)
0.3010299957 = 0.0251284018t
Divide both sides by 0.0251284018
0.3010299957 = 0.0251284018t
= t
11.97967138 = t
or approximately 12 years.
Edwin
