Respuesta :
Answer:
Step-by-step explanation:
We'll first find out how long it takes for the account to have 2500 in it, then we'll add a year (we'll check ourselves anyway, just to be sure!) This is an exponential growth problem of the form
[tex]A(t)=P(1+r)^t[/tex] since the compounding is only done once a year. Filling in:
[tex]2500=2000(1.02)^t[/tex] Begin by dividing both sides by 2000 to get
[tex]1.25=(1.02)^t[/tex] In order to get that t down from its current position in the equation, we will take the natural log of both sides. This allows us to pull the t down and put it out front like this:
ln(1.25) = t ln(1.02) Now divid both sides by ln(1.02) and you will see that
t = 11 years. At 11 years (rounded), the account will have
[tex]A(t)=2000(1.02)^{11}[/tex] = 2486.75 and after 12 years:
[tex]A(t)=2000(1.02)^{12[/tex] = 2536.48
t = 12 works!
The minimum number of complete years it would take the investment to increase to $2500 is 12 years.
Definition of compound interest
Compound interest is when both the principal and the interest earned increases in value at the interest rate per period.
Formula for determining the number of years
Number of years = In(FV / PV) ÷ r
- FV = future value
- PV = present value
- r = interest rate
In(2500 / 2000) ÷ 0.02
In (1.25) ÷ 0.02
= 11.2 years
= 12 years
To learn more about compound interest, please check: https://brainly.com/question/18760477
