Solve the problem.
-A college loan of $\$ 26,000$ is made at $4 \%$ interest, compounded annually. After t years, the amount due, $A$, is given by the function $A ( t ) = 26,000 ( 1.04 ) ^ { t } \text {. }$ After what amount of time will the amount reach $\$ 41,000$ ? Round your answer to the nearest tenth.
A) $0.1 \mathrm { yr }$
B) $11.6 \mathrm { yr }$
C) $70.3 \mathrm { yr }$
D) $0.4 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the time $t$ when the amount reaches \$41,000, set $A(t) = 41,000$ and solve for $t$: $41,000 = 26,000(1.04)^t$. Dividing both sides by 26,000 gives $1.5769 = (1.04)^t$. Taking the logarithm of both sides and solving for $t$ yields $t \approx 11.6$ years.

Solve the Problem $26,000\$ 26,000$26,000 Is Made At 4%4 \%4% Interest, Compounded Annually

Solve the Problem $\$ 26,000$ Is Made At $4 \%$ Interest, Compounded Annually