The initial investment in a savings account in which interest is compounded continuously is $\$ 604$. If the time required to double the amount is $9 \frac { 1 } { 2 }$ years, what is the amount after 15 years? Round your answer to the nearest cent.
A) $\$ 1,917.58$
B) $\$ 1,804.46$
C) $\$ 1,907.37$
D) $\$ 1,404.46$
E) $\$ 8,278.18$

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $ A = Pe^{rt} $. Given that the amount doubles in $9.5$ years, we find the rate $ r $ using $ 2 = e^{9.5r} $. Solving gives $ r \approx 0.07296 $. Then, calculate $ A = 604 \times e^{0.07296 \times 15} \approx 1804.46 $.

The Initial Investment in a Savings Account in Which Interest $604\$ 604$604

The Initial Investment in a Savings Account in Which Interest $\$ 604$