SOLUTION: Can you please help me with this:) 1. Chris invests $10 000 at 7.2% per year, with monthly compounding periods. How long will it take for his investment to grow to $25 000?

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Question 1088272: Can you please help me with this:)

1. Chris invests $10 000 at 7.2% per year, with monthly compounding periods. How long will it take for his investment to grow to $25 000?


Found 2 solutions by jim_thompson5910, addingup:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We're given:
A = 25000 which is the amount we want after some time (t)
P = 10000 which is the initial deposit (aka principal)
r = 7.2% = 0.072 is the interest rate; we'll use the decimal form
n = 12 to indicate monthly compounding, or 12 times a year compounding

The goal is to find t.

A+=+P%2A%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula

25000+=+10000%2A%281%2B0.072%2F12%29%5E%2812%2At%29 Plug in all of the given values

25000+=+10000%2A%281%2B0.006%29%5E%2812%2At%29

25000+=+10000%2A%281.006%29%5E%2812%2At%29

%2825000%29%2F%2810000%29+=+%281.006%29%5E%2812%2At%29 Divide both sides by 10000

2.5+=+%281.006%29%5E%2812%2At%29

%281.006%29%5E%2812%2At%29=2.5 Flip the equation

log%28%28%281.006%29%5E%2812%2At%29%29%29=log%28%282.5%29%29 Apply logs to both sides

%2812%2At%29%2Alog%28%281.006%29%29=log%28%282.5%29%29 Use one of the log rules to pull down the exponent

12%2At=%28log%28%282.5%29%29%29%2F%28log%28%281.006%29%29%29 Divide both sides by log(1.006)

12%2At=%280.39794%29%2F%280.002598%29 Get the approximate log values

12%2At=153.171671

t=%28153.171671%29%2F%2812%29 Divide both sides by 12

t=12.764306

It will take about 12.764306 years. If you round to the neaest whole year, then it will take 13 years.


Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
A = Accrued amount (principal + interest, in this case 25000
P = Principal (initial amount, in this case 10000)
r = rate 0.072
n = number of compounding periods (12)
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In the compound interest formula, time is an exponent:
A = P(1+(r/n))^(nt)
In order to solve for an exponent we have to use logarithms.
Take the formula above, do a little algebra on it, and you get:
t = ln(A/P)/n[ln(1+r/n)] = [ln(A)-ln(P)]/n[ln(1+r/n)]
Now just plug in your numbers:
t = [ln(25000/10000)]/[12(ln(1+(0.072/12)))]
t = (ln25000-ln10000)/12(ln(1+0.006))
t = 10.12-9.21/(0.072)
t = 12.64 years