Respuesta :
The number of years is 4.781 in which $21,136.18 amount to $75,514.55 at 27.54% per annum when compounded quarterly and this can be determined by using the formula of the compound interest.
Given :
- Principal amount = $21136.18
- Final amount = $75514.55
- Interest rate per annum = 27.54%
- Compounded quaterly.
The formula of the compound interest is given by:
[tex]\rm A= P(1+\dfrac{r}{n})^{nt}\\[/tex]
where A is the final amount, P is the principal amount, r is the interest rate, t is the time in years, and 'n' is a number of times interest applied.
Now, substitute the values of known terms in the above formula.
[tex]\rm 75514.55= 21136.18(1+\dfrac{0.2754}{4})^{4\times t}\\[/tex]
[tex]3.5727=(1.06885)^{4t}[/tex]
Now, take the log on both sides.
[tex]\rm log(3.5727)=(4t)log(1.006885)[/tex]
19.1237 = 4t
t = 4.781 years
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/14295570
