SOLUTION: Please help me solve this: how long will it take your money to grow from $150 to $200 when it is invested at 3% compounded quarterly? I've gotten as far as {{{ 200/150=(1+0.03/

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Please help me solve this: how long will it take your money to grow from $150 to $200 when it is invested at 3% compounded quarterly? I've gotten as far as {{{ 200/150=(1+0.03/      Log On

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Question 920671: Please help me solve this: how long will it take your money to grow from $150 to $200 when it is invested at 3% compounded quarterly?
I've gotten as far as +200%2F150=%281%2B0.03%2F4%29%5E4t+ thank you
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A, amount; p, principal, t, how many time compounding periods to reach A.

highlight_green%28A=p%281%2B0.03%2F4%29%5E%28t%29%29; this is what you are trying to express.
Note that the quarterly interest rate is one fourth of the yearly rate, and the
number of compounding periods is t.

Sovle for t, and then substitute A=200 and p=150.

Some of the algebraic steps:
A=p%281.0075%29%5E%28t%29
1.0075%5E%28t%29=A%2Fp
You can choose any logarithm base desired.
log%28%28%281.0075%29%5E%28t%29%29%29=log%28%28A%2Fp%29%29
t%2Alog%28%281.0075%29%29=log%28%28A%2Fp%29%29
t=%28log%28%28A%2Fp%29%29%2Flog%28%281.0075%29%29%29
highlight%28t=log%28%28A%2Fp%29%29%2F%28log%28%281.0075%29%29%29%29

TIME PERIODS: highlight%28t=38.5%29
which is 9.625 years, but in strict amount of quarter periods of the year, highlight%289%263%2F4%29 years.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+200%2F150=%281%2B0.03%2F4%29%5E%284t%29+ where t= number of years
4%2F3=1.0075%5E%284t%29+
log%28%284%2F3%29%29=4t%2Alog%28%281.0075%29%29
4t=log%28%28%224%2F3%22%29%29%2Flog%28%281.0075%29%29
t=log%28%28%224%2F3%22%29%29%2F%284%2Alog%28%281.0075%29%29%29
t=9.62 (rounded)
It should take a little longer, because over 9.5 years,
That is 4%2A9.5=38 quarters, the $150 would grow to
150%2A1.075%5E38=199.25 (rounded).
Then to earn the remaining $0.75, at 3% you would need x years,
with 199.25%2A0.03%2Ax=0.75
x=0.75%2F%28199.25%2A0.03%29=0.13 (rounded),
for a total of 9.5%2B0.13=9.63 years.