Solve the problem.
-A college loan of $\$ 25,000$ is made at $4 \%$ interest, compounded annually. After tyears, the amount due, $\mathrm{A}$, is given by the function
$$\mathrm{A}(\mathrm{t})=25,000(1.04)^{\mathrm{t}}$$
After what amount of time will the amount reach $\$ 37,000$ ? Round your answer to the nearest tenth.
A) $0.1 \mathrm{yr}$
B) $0.4 \mathrm{yr}$
C) $10.0 \mathrm{yr}$
D) $68.7 \mathrm{yr}$

Question

Quizplus · Accepted Answer

To find the time $t$ when the amount reaches \$37,000, we set $A(t) = 37,000$ and solve for $t$:$$37,000 = 25,000(1.04)^t$$Dividing both sides by 25,000 gives:$$1.48 = (1.04)^t$$Taking the logarithm of both sides:$$\log(1.48) = t \log(1.04)$$Solving for $t$ gives:$$t = \frac{\log(1.48)}{\log(1.04)} \approx 10.0 \text{ years}$$

Solve the Problem $25,000\$ 25,000$25,000 Is Made At 4%4 \%4% Interest, Compounded Annually

Solve the Problem $\$ 25,000$ Is Made At $4 \%$ Interest, Compounded Annually