Question

In how many years will $ 21,136.18 amount to $ 75,514.55 at 27.54 % per annum when compounded quarterly?

Answer 1

Answer:

A. 4.781 years

Step-by-step explanation:

Answer 2

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:

$\rm A= P(1+\dfrac{r}{n})^{nt}$

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.

$\rm 75514.55= 21136.18(1+\dfrac{0.2754}{4})^{4\times t}$

$3.5727=(1.06885)^{4t}$

Now, take the log on both sides.

$\rm log(3.5727)=(4t)log(1.006885)$

19.1237 = 4t

t = 4.781 years

Therefore, the correct option is B).

For more information, refer to the link given below:

brainly.com/question/14295570