Question 1183161
Find the time required for an investment of 5000 dollars to grow to 6500 dollars at an interest rate of 4.4 percent per year, compounded monthly.
:
Use the compound interest formula: {{{p(1+(r/n))^(nt)}}} = A; where
A = resulting amt after t time
p = initial amt
r = annual interest rate in decimal form
n = compound periods per yr
t = time in yrs
:
{{{5000(1+(.044/12))^(12*t)}}} = 6500
{{{(1.00367)^(12t)}}} = {{{6500/5000}}}
{{{(1.00367)^(12t)}}} = 1.3
using natural logs
12t*ln(1.00367) = ln(1.3)
12t = {{{ln(1.3)/ln(1.00367)}}}
use your calc
12t = 71.62
t = {{{71.72/12}}}
t = 5.968 ~ 6 yrs for 5k to grow to 6.5k