<PRE><B>Question 144533</B>
Find the rate that a bank offers if $1000 is tripled in 8 years. Assume the interest is compounded quarterly. Using this formula :
a = {{{p(1+r/n)^(nt)}}}
where
n = 4
t = 8
Since they just want to find out at what rate it triples just assign:
a = 3
p = 1
:
Write it:
{{{1*(1+r/4)^(4*8)}}} = 3
or just:
{{{(1+r/4)^32}}} = 3
Find the log of both sides:
log{{{((1+r/4)^32)}}} = log(3)
:
The log equiv of exponents
32*log{{{(1+r/4)}}} = log(3)
:
Find the log of 3
32*log{{{(1+r/4)}}} = .477121
:
Divide both sides by 32:
log{{{(1+r/4)}}} = {{{.477121/32}}}
:
{{{(1+r/4)}}} = .01491
;
Find {{{10^x}}} of .01491 on a calc:
1 + {{{r/4}}} = 1.0349
:
Subtract 1 from both sides:
{{{r/4}}} = .0349
:
Multiply both sides by 4:
r = .0349 * 4
:
r = .1397 or 13.97 ~ 14%
:
:
Check solution on a calc: enter (1+(14/4))^32 = 3.0067 ~ 3</PRE>