SOLUTION: Find out how many years it takes $1800 to double at 3.2% interest compounded weekly. Use equation: A=P(1+r/n)^nt Show all steps.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find out how many years it takes $1800 to double at 3.2% interest compounded weekly. Use equation: A=P(1+r/n)^nt Show all steps.       Log On


   

Question 868846: Find out how many years it takes $1800 to double at 3.2% interest compounded weekly.
Use equation: A=P(1+r/n)^nt
Show all steps.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You want the formula this way: A=P(1+r/n)^(nt)
and as rendered, is A=P%281%2Br%2Fn%29%5E%28nt%29.

n is the number of compounding for a year.
t is time in years.
r is the interest rate as a decimal number.
P is "principle", starting amount.


You want to find t for n=52, P=1800, and r=0.032. A=2*P=3600.
Whether Natural log or Common log is your choice. You SHOULD solve for t symbolically, first; and then substitute the values.

My choice is log base 10.
log%28%28A%29%29=log%28%28P%29%29%2Blog%28%28%281%2Br%2Fn%29%5E%28nt%29%29%29
log%28%28A%29%29=log%28%28P%29%29%2Bnt%2Alog%28%281%2Br%2Fn%29%29
nt%2Alog%28%281%2Br%2Fn%29%29=log%28%28A%29%29-log%28%28P%29%29
nt%2Alog%28%281%2Br%2Fn%29%29=log%28%28A%2FP%29%29, and you know that A%2FP will be 2, so make that change now.
nt%2Alog%28%281%2Br%2Fn%29%29=log%28%282%29%29
t=%281%2Fn%29%281%2Flog%28%281%2Br%2Fn%29%29%29log%28%282%29%29
highlight%28t=%281%2Fn%28log%28%281%2Br%2Fn%29%29%29%29log%28%282%29%29%29-----these steps and result can look much better on paper or display wall.

Now substitute the values.
t=%281%2F52log%28%281%2B0.032%2F52%29%29%29%2Alog%28%282%29%29
should be 21%262%2F3 year or 21 years 8 months

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find out how many years it takes $1800 to double at 3.2% interest compounded weekly.
Use equation: A=P(1+r/n)^nt
Show all steps. 


Doesn't matter what amount is used, the outcome is the same. All that matters is whether the initial investment

or P, is doubled or tripled, the compounding periods, and the interest rate.

A+=+P%281+%2B+r%2Fn%29%5Ent

2P+=+P%281+%2B+r%2Fn%29%5Ent

2P+=+P%281+%2B+.032%2F52%29%5E%2852t%29

2+=+%281+%2B+.032%2F52%29%5E%2852t%29

2+=+1.000615%5E%2852t%29 -------- Exponential form

log+%281.000615%2C+2%29+=+52t ------ Logarithmic form

highlight_green%28t+=+%28log+2%29%2F%28log+1.000615%29%29 ÷ highlight_green%2852%29