Solve.
-Find out how long it takes a $\$ 3000$ investment to earn $\$ 400$ interest if it is invested at $9 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { n t }$.
A) $1.6$ years
B) $1.8$ years
C) $1.2$ years
D) $1.4$ years

Question

Quizplus · Accepted Answer

The formula for compound interest is used to find the time $ t $. Given $ A = 3400 $, $ P = 3000 $, $ r = 0.09 $, and $ n = 2 $, solve for $ t $ in $ 3400 = 3000 \left( 1 + \frac{0.09}{2} \right)^{2t} $. This simplifies to $ 1.1333 = 1.045^{2t} $. Taking the natural logarithm of both sides and solving for $ t $ gives approximately $ 1.4 $ years.

Solve -Find Out How Long It Takes A $3000\$ 3000$3000 Investment to Earn

Solve
-Find Out How Long It Takes A $\$ 3000$ Investment to Earn