Question 275383
Find the number of years it will take for $31,000 to grow to 33,405.06 at 3% interest compounded quarterly.
:
Let's see what I get:
:
The compound interest formula: A = {{{P(1 + (r/n))^(nt))}}}
Where
A = resulting amt
P = principal
r = interest rate in decimal form
n = no. times compounded per year
t = no. of years
:
{{{31000(1 + (.03/4))^(4t))}}} = 33405.06
{{{31000(1.0075)^(4t))}}} = 33405.06
{{{(1.0075)^(4t))}}} = {{{33405.06/31000}}}
{{{(1.0075)^(4t))}}} = 1.0775826
{{{log(1.0075)^(4t))}}} = log(1.0775826)
4t*log(1.0075) = log(1.0775826)
4t = {{{log(1.0775826)/log(1.0075)}}}; use the calc here
4t = 10.00
t = {{{10/4}}}
t = 2.5 yrs