Question

Sung Lee invests $3,000 at age 18. He hopes the investment will be worth $6,000 when he turns 25. 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:

10.4%

Step-by-step explanation:

Sung Lee invests $3,000 at age 18.

He hopes the investment will be worth $6,000 when he turns 25, that is, after 7 years.

The interest compounds (Compound Interest). The formula for the final amount in a compound interest is:

$A = P(1 + R)^T$

where P = Principal (Amount invested) = $3000

A = final amount = $6000

R = rate

T = number of years = 7 years

This implies that:

$6000 = 3000(1 + R)^7\\\\\frac{6000}{3000} = (1 +R)^7\\\\2 = (1 + R)^7$

Find the 7th root of 2:

$\sqrt[7]{2} = (1 + R)\\\\1.104 = (1 + R)\\\\=> R = 1.104 - 1\\\\R = 0.104$

=> R = 10.4%

Hence, the rate would need to be 10.4% for him to achieve his goal.