Question

1. trevor opened a savings account and deposited $100.00 as principal. the account earns 8% interest, compounded continuously. how much interest will he earn after 6 years?
2. use the formula $a = pe^{rt}$, where a is the balance (final amount), p is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
3. round your answer to the nearest cent.
4. $

Explanation:

Step1: Identify given values

$P = 100$, $r = 0.08$, $t = 6$

Step2: Calculate final balance $A$

$$A = Pe^{rt} = 100e^{0.08 \times 6} = 100e^{0.48}$$
Using $e \approx 2.71828$, $e^{0.48} \approx 1.61607$, so $A \approx 100 \times 1.61607 = 161.607$

Step3: Calculate earned interest

Subtract principal from final balance: $161.607 - 100 = 61.607$

Step4: Round to nearest cent

Round $61.607$ to two decimal places: $61.61$

Answer:

$\boldsymbol{\$61.61}$