Chris invests $10 000 at 7.2%/a compounded monthly. How long will it take for his investment to grow to $25 000?
7.2 % per annum, compounded monthly corresponds to a rate of .072/12 or .006 per month
so we have:
10000(1.006)^n = 25000 , where n is the number of months
1.006^n = 2.5
take log of both sides
log (1.006)^n = log 2.5
n log 1.006 = log 2.5
n = log 2.5/log1.006 = appr 153 months
To figure out how long it will take for Chris's investment to grow to $25,000, we need to use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount ($25,000 in this case)
P = Principal amount (initial investment of $10,000)
r = Annual interest rate (7.2% in decimal form, which is 0.072)
n = Number of compounding periods per year (12 since it is compounded monthly)
t = Number of years
Since we want to find how long it will take (t), we need to rearrange the formula:
t = (log(A/P))/(n * log(1 + r/n))
Now we can plug in the values and solve for t:
t = (log(25000/10000))/(12 * log(1 + 0.072/12))
t = (log(2.5))/(12 * log(1.006))
Using a calculator to evaluate this expression, we find:
t ≈ 9.78
Therefore, it will take approximately 9.78 years for Chris's investment to grow to $25,000 at a 7.2% annual interest rate compounded monthly.
To find out how long it will take for Chris's investment to grow to $25,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($25,000)
P = the principal amount ($10,000)
r = the annual interest rate (0.072)
n = the number of times the interest is compounded per year (12 for monthly compounding)
t = the number of years
Plugging in the values:
$25,000 = $10,000(1 + 0.072/12)^(12t)
Now, we can solve for t.