Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$
-$\$ 3500$ is invested at $5 \%$ compounded quarterly. In how many years will the account have grown to $\$ 8000$ ? Round to the nearest tenth of a year.
A) $22.0 \mathrm { yr }$
B) $16.6 \mathrm { yr }$
C) $1.2 \mathrm { yr }$
D) $16.9 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To solve for $t$, we use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ with $A = 8000$, $P = 3500$, $r = 0.05$ (5% as a decimal), and $n = 4$ (compounded quarterly). Rearranging for $t$, we get $t = \frac{\log(A/P)}{n \log(1 + r/n)}$. Plugging in the values, $t$ calculates to approximately $16.6$ years.

Use the Formula A A=P(1+rn)nt to solve. A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }A=P(1+nr​)nt to solve.

Use the Formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { to solve. }$