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.

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:

where P = Principal (Amount invested) = $3000

A = final amount = $6000

R = rate

T = number of years = 7 years

This implies that:

Find the 7th root of 2:

=> R = 10.4%

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

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step-by-step explanation:

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