Question

Sung Lee invests $7,000 at age 18. He hopes the investment will be worth $14,000 when he turns 30. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

Answer 1

Answer:

2.3%

Step-by-step explanation:

For continous compound interest

$A=Pe^{it}$

Where A is final value, P is initial investment, i is interest rate in decimal and t is period.

The time will be 30-18=12 years

Substituting $14000 for A, $7000 for P and 12 years for t

$14000=7000e^{12i}\\e^{12i}=2$

Introducing natural logarithms on both sides then 12i=ln 2

Making i the subject of formula then

i=ln 2 ÷12=0.05776226504666

The percentage rounded off will be 5.7% p.a