Solve.
-Find out how long it takes a $\$ 2900$ investment to earn $\$ 400$ interest if it is invested at $7 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$.
A) $2.1$ years
B) $1.7$ years
C) $1.9$ years
D) $2.3$ years

Question

Quizplus · Accepted Answer

To solve for the time $t$, we use the given formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$, where $A$ is the final amount, $P$ is the principal amount (\$2900), $r$ is the annual interest rate (0.07 for 7%), $n$ is the number of times the interest is compounded per year (2 for semiannually), and $t$ is the time in years. The final amount $A$ is the principal plus interest, which is \$2900 + \$400 = \$3300. Plugging in the values, we get:$$3300 = 2900 \left(1 + \frac{0.07}{2}\right)^{2t}$$Solving for $t$ gives approximately $1.9$ years.

Solve -Find Out How Long It Takes A $2900\$ 2900$2900 Investment to Earn

Solve
-Find Out How Long It Takes A $\$ 2900$ Investment to Earn