Question

An internet investment company advertises that if you invest your money with them at 14%, compounded annually, they guarantee yo double your money sooner than you can imagine. Ignoring taxes, how long would it take to double your money at a simple rate of 14% compounded annually?

a. approx 3.5 yrs
b. approx 5 yrs
c. exactly 7 yrs
d. approx 10 yrs
e. Exactly 14 yrs

I chose b. approx 5 yrs pretending that my initial investment was $5k: 5,000+700 (1), 5700+798 (2), 6498+909.72 (3), 7407.72+1037.0808 (4), 8444.8008+1182.27 (5)
9627.07+1347.79= $10,974.863

Am I correct?

Answer 1

For simple interest
2P=P+0.14tP
0,14t=1 t= approx 7 yrs

For compound interest
2P=P(1.14)^t
1.14^t=2
t=ln(2)/ln(1.14)=5.29 approx 5 yrs