Calculating Interest 
A person deposited $5000\$$ at $10\%$ simple interest for $2$ years. How much more money will she have in her account at the end of two years, if it is compounded semi-annually? $50/40/77.5/85.5$

My attempt: $\dfrac{5000*10*2}{100}=1000,$ so amount$=6000.$ $5000\left(1+\dfrac{10}{2*100}\right)^{2*2}=5000\left(\dfrac{21}{20}\right)^4=6077.5\$$. So, answers is $77.5\$$.
My query: Can we have a quicker way to solve this question? In my approach, the calculation is lengthy. Multiplying $21$, $4$ times is time-consuming.
P.S- It is actually a MCQ and one question should be solved in less than $1$ minute and calculator is not allowed.

Edit: Some time after the answer below, the question was changed to specify no calculator. In that case, one can square $1.05$, getting $1.1025$, and square again. The squaring of $1.1025$ can be done conventionally.  We don't have to pay much attention to the digits on the right. 
You can also use the second order approximation $(1+x)^4\approx 1+4x+6x^2$ for $x$ reasonably close to $0$. This will get you close enough.

Answer before "no calculator" was specified:
You can use the $x^y$ button on your calculator, it it has one. All scientific and financial calculators do.  Or you can press the $x^2$ button twice. 
Note that Google has a nice calculator. If in the search window you type (1.05)^4 it will do the calculation. 
Remark: The answer should be rounded to the nearest cent. It would be good to drop the "percent" notation and think of the interest rate as $0.10$. So when we compound every half-year, the interest rate is $0.05$.
It follows that in $4$ compounding periods our $5000$ grows to $5000(1.05)^4$. 
