Answer:
[tex]t=14.2\ years[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\ P=\$500,000\\ r=0.05\\n=1\\ A=\$1,000,000[/tex]
substitute in the formula above and solve for t
[tex]1,000,000=500,000(1+\frac{0.05}{1})^{(1)t}[/tex]
[tex]2=(1.05})^{t}[/tex]
Apply log both sides
[tex]log(2)=log[(1.05})^{t}][/tex]
[tex]log(2)=(t)log(1.05)[/tex]
[tex]t=log(2)/log(1.05)[/tex]
[tex]t=14.2\ years[/tex]
Answer:
~14.2066 years
Step-by-step explanation:
assuming p.a. means per annual:
$500,000 with intrest rate 5% per year. how many years for money to become $1,000,000?
with annual intrest, a percentage of the money you invest is added to your balance every year
set up equation: (original money*(1+ intrest rate))^x=goal money
there is a 1 because you are adding on to the original (100%) amount of money
x is the number of years untill goal money. is an exponent because it depends on the previous years balance. note that amount of money gained will change per year.
50,000*(1+0.05)^x=1,000,000
solve------
divide by 50,000 both sides
1*(1+0.05)^x=2
(1+0.05)^x=2
(1.05)^x=2
apply log_1.05 to both sides
log_1.05 (1.05)^x= log_1.05 2
x= log_1.05 2
use calculator to approx
~14.2067 years
hope this helps
