Compute the compound interest.
-How long must $\$ 5900$ be in a bank at $6 \%$ compounded annually to become $\$ 9967.93$ ? (Round to the nearest year.)
A) $9 \mathrm{yr}$
B) $8 \mathrm{yr}$
C) $10 \mathrm{yr}$
D) $11 \mathrm{yr}$

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + r/n)^{nt}$, where $A$ is the final amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times per year that the interest is compounded, and $t$ is the number of years.In this case, we have $P = 5900$, $A = 9967.93$, $r = 0.06$, and $n = 1$. Solving for $t$, we get:$$9967.93 = 5900(1 + 0.06/1)^{1t}$$$$9967.93 = 5900(1.06)^t$$$$\frac{9967.93}{5900} = 1.06^t$$$$1.691176 = 1.06^t$$$$t = \log_{1.06} 1.691176$$$$t \approx 9$$Therefore, the correct answer is A) $9 \mathrm{yr}$.

Compute the Compound Interest $5900\$ 5900$5900 Be in a Bank At 6%6 \%6%

Compute the Compound Interest $\$ 5900$ Be in a Bank At $6 \%$