Respuesta :
Answer:
14
Step-by-step explanation:
10000 = 5000[tex](1.05)^{t}[/tex]
2 = [tex](1.05)^{t}[/tex]
ln(2) = t ln(1.05)
t = ln(2)/ln(1.05)
[tex]\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots[/tex]
For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.
How to find the compound interest?
If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,
then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
For $5000 invested at 5% p.a. compound interest with yearly
rests to double in value, we need to find the time.
So,
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
[tex]10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21[/tex]
Hence, The time will be 14 years. So, option D is correct.
Learn more about compound interest here:
https://brainly.com/question/1329401
#SPJ2
