SOLUTION: Find the rate that a bank offers if $1000 is tripled in 8 years. Assume the interest is compounded quarterly. Using this formula nt a=p(1+r/t)

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Question 144533: Find the rate that a bank offers if $1000 is tripled in 8 years. Assume the interest is compounded quarterly. Using this formula
nt
a=p(1+r/t)

this is what I got so far
a=3p
p=1000
r=?
n=4
t=8
4(8)
3p=p(1+r/t)
32
3=(1+r/4)
32
3=1.25r
do I take the log of both sides??
I'm lost
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%281%2Br%2Fn%29%5E%28nt%29
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%2A%281%2Br%2F4%29%5E%284%2A8%29 = 3
or just:
%281%2Br%2F4%29%5E32 = 3
Find the log of both sides:
log%28%281%2Br%2F4%29%5E32%29 = log(3)
:
The log equiv of exponents
32*log%281%2Br%2F4%29 = log(3)
:
Find the log of 3
32*log%281%2Br%2F4%29 = .477121
:
Divide both sides by 32:
log%281%2Br%2F4%29 = .477121%2F32
:
%281%2Br%2F4%29 = .01491
;
Find 10%5Ex of .01491 on a calc:
1 + r%2F4 = 1.0349
:
Subtract 1 from both sides:
r%2F4 = .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