Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $4,600 for 6 years at 3%. The choices are rounded to the nearest cent.
A) $9,362.24
B) $3,671.47
C) $8,260.80
D) $5,507.20
E) $3,239.53

Question

Quizplus · Accepted Answer

Using the formula $A = p e ^ { r t }$, where $A$ is the amount of money accumulated after n years, including interest, $p$ is the principal amount ($4,600), $r$ is the annual interest rate (3%, or 0.03 as a decimal), and $t$ is the time the money is invested or borrowed for, in years (6 years). Plugging in the values: $A = 4600 \cdot e ^ {0.03 \cdot 6}$. Calculating this gives $A \approx 5507.20$, which matches choice D.

Use the Formula A=pertA = p e ^ { r t }A=pert

Use the Formula $A = p e ^ { r t }$