Respuesta :
34 years will the account reach $1500, if An initial investment of $1000 is deposited in an account with a 1.2% interest rate, compounded annually.
Step-by-step explanation:
The given is,
Initial investment of $1000
Interest rate 1.2%, compounded annually
Future amount $1500
Step:1
Formula to calculate the future amount with an interest rate of compounded annually,
[tex]F=P(1+\frac{r}{n} )^{nt}[/tex]............................(1)
Where,
F - Future worth amount
P - Initial investment
r - Rate of interest
n - No.of compounding in a year
t - No.of years
From given,
F = $1500
P = $1000
r = 1.2%
n = 1 (compounded annually)
Equation (1) becomes,
[tex]1500=1000(1+\frac{0.012}{1} )^{(1)(t)}[/tex]
[tex]\frac{1500}{1000} =(1+\frac{0.012}{1} )^{(t)}[/tex]
[tex]1.5 =(1+\frac{0.012}{1} )^{(t)}[/tex]
[tex]1.5 =(1+0.012 )^{(t)}[/tex]
[tex]1.5 =(1.012 )^{(t)}[/tex]
Take log on both sides,
[tex]log 1.5 = {(t)} log (1.012 )[/tex]
Substitutes log values,
0.17609126 =( t ) 0.0051805
[tex]t = \frac{0.17609126}{0.0051805}[/tex]
t = 33.99
t ≅ 34 years
Result:
34 years will the account reach $1500, if An initial investment of $1000 is deposited in an account with a 1.2% interest rate, compounded annually.
