Answer:
Step-by-step explanation:
The formula you need for this is
[tex]A(t)=P(1+\frac{r}{n})^{nt[/tex] where
A(t) is the amount after a certain number of years has gone by,
P is the initial deposit,
r is the interest rate in decimal form,
n is the number of compoundings done per year, and
t is the amount of time in years.
For us,
A(t) = 11900
P is 250
r is .048
n is 12 (there are 12 months in a year)
t is our unknown. Filling in:
[tex]11900=250(1+\frac{.048}{12})^{(12)(t)[/tex] which simplifies a bit to
[tex]11900=250(1_.004)^{(12t)[/tex] . Now we'll divide both sides by 250:
[tex]47.6=(1.004)^{12t[/tex] and then take the natural log of both sides to bring that t down out front:
[tex]ln(47.6)=ln(1.004)^{12t[/tex] and then
ln(47.6) = 12t ln(1.004). Now divide both sides by ln(1.004) to isolate the 12t:
967.6383216 = 12t and divide both sides by `12 to get
t = 80.6 months which is 6.7 years
