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:
[tex]A = P(1 + R)^T[/tex]
where P = Principal (Amount invested) = $3000
A = final amount = $6000
R = rate
T = number of years = 7 years
This implies that:
[tex]6000 = 3000(1 + R)^7\\\\\frac{6000}{3000} = (1 +R)^7\\\\2 = (1 + R)^7[/tex]
Find the 7th root of 2:
[tex]\sqrt[7]{2} = (1 + R)\\\\1.104 = (1 + R)\\\\=> R = 1.104 - 1\\\\R = 0.104[/tex]
=> R = 10.4%
Hence, the rate would need to be 10.4% for him to achieve his goal.
