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:
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.
Now, take the log on both sides.
19.1237 = 4t
t = 4.781 years
Therefore, the correct option is B).
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