Question

If you were to place $2500 in a savings account that pays 3% interest compound continually how much money will you have after 5 years. Assume you make no other deposits or withdrawals.

Answer 1

`\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ t=years\dotfill &5 \end{cases} \\\\\\ A=2500e^(0.03\cdot 5)\implies A=2500e^(0.15)\implies A\approx 2904.59`

Answer 2

C. $2904.59

Explanation:

Compounded continually means that the principal amount is constantly earning interest and the interest keeps earning on the interest earned.

The formula to apply is

`A=Pe^(rt)`

where A is the amount, P is the principal, r is rate of interest, t is time in years and e is the mathematical constant

Taking

e=2.7183, P=$2500, r=3% and t=5 years

`A=Pe^(rt) \\\\\\A=2500*2.7183^(0.03*5) \\\\\\A=2500*1.1618\\\\\\A=2904.59\\\\A=2904.59`