Solve the problem.
-Find out how long it takes a $2,700 investment to double if it is invested at 7% compounded semiannually. Round to the nearest tenth of a year. Use the formula $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$
A) 9.9 years
B) 10.3 years
C) 10.5 years
D) 10.1 years

Question

Quizplus · Accepted Answer

Using the compound interest formula, set A = 5400, P = 2700, r = 0.07, and n = 2. Solve for t: $5400 = 2700(1 + \frac{0.07}{2})^{2t}$. Simplifying gives $2 = (1.035)^{2t}$. Taking the natural log of both sides and solving for t gives approximately 10.1 years.

Solve the Problem A=P(1+rn)nt\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }A=P(1+nr​)nt

Solve the Problem $\mathrm { A } = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { \mathrm { nt } }$