How many years will it take for $12,000 to grow to $15,000 at 5.75% compounded monthly?
Use the compound interest formula for
n=number of periods
R=monthly interest rate, 5.75%/12=0.479167%
P=present value of investment = $12000
F=future value of investment = $15000
Then
F=ARn
15000=12000(1.00479167)n
1.00479167n = 15000/12000=1.25
take log on both sides
n*log(1.00479167)=log(1.25)
n=log(1.25)/log(1.00479167)
=46.68 months
=4 years (approx.)
hummm...i think this question is wrong....whats your suggestion..i m waiting for your reply...thanks
CAMY
To find out how many years it will take for $12,000 to grow to $15,000 at a compounded interest rate of 5.75% per year, compounded monthly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $12,000, the future value (A) is $15,000, the annual interest rate (r) is 5.75% (or 0.0575 as a decimal), and the interest is compounded monthly (n=12).
Plugging in these values into the formula:
$15,000 = $12,000(1 + 0.0575/12)^(12t)
Now, let's solve for t.
Divide both sides of the equation by $12,000:
$15,000/$12,000 = (1 + 0.0575/12)^(12t)
1.25 = 1.00479^(12t)
Next, take the natural logarithm (ln) of both sides:
ln(1.25) = ln(1.00479^(12t))
Using the logarithmic identity ln(a^b) = b ln(a):
ln(1.25) = 12t ln(1.00479)
Divide both sides by ln(1.00479):
ln(1.25) / ln(1.00479) = 12t
Finally, solve for t by dividing both sides by 12:
t = ln(1.25) / (12 ln(1.00479))
Using a calculator, we can find that the value of t is approximately 4.33 years.
Therefore, it will take approximately 4.33 years for $12,000 to grow to $15,000 at a 5.75% interest rate, compounded monthly.