Suppose $\$ 9000$ is invested at $7.25 \%$ annual interest, compounded continually. (i) What will be the amount in the account in 6 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.
A) $\$ 9676.74$; (ii) 15.2 years
B) $\$ 9000.00$; (ii) 12.6 years
C) $\$ 4018.03$; (ii) 5.6 years
D) (i) $\$ 13,904.67$; (ii) 9.6 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is deposited or borrowed for, in years. For (i), substituting $P = 9000$, $r = 0.0725$, and $t = 6$ into the formula gives $A = 9000e^{(0.0725)(6)}$, which calculates to approximately $\$13,904.67$. For (ii), to find when the principal doubles, set $A = 2P = 18000$, and solve for $t$, giving $18000 = 9000e^{(0.0725)t}$. Solving for $t$ gives approximately $9.6$ years.

Suppose $9000\$ 9000$9000 Is Invested At 7.25%7.25 \%7.25% Annual Interest, Compounded Continually $9676.74\$ 9676.74$9676.74

Suppose $\$ 9000$ Is Invested At $7.25 \%$ Annual Interest, Compounded Continually $\$ 9676.74$