(Advanced analysis) Ricardo deposits $1,000 into his savings account. What rate of interest would he have to earn on his savings for his deposit to be worth $2,000 in eight years?
A) 8.75 percent
B) 9.1 percent
C) 10 percent
D) 10.4 percent

Question

Quizplus · Accepted Answer

To find the rate of interest required to double the deposit in eight years, we can use the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $n$ is the number of years the money is invested for. We want to solve for $r$ when $A = 2000$, $P = 1000$, and $n = 8$. Plugging in the values, we get $2000 = 1000(1 + r)^8$. Simplifying, we get $2 = (1 + r)^8$. Taking the 8th root of both sides, we find $1 + r = 2^{1/8}$. Solving for $r$, we get $r = 2^{1/8} - 1$, which is approximately 0.09 or 9%, making the closest option B) 9.1 percent.

(Advanced Analysis) Ricardo Deposits $1,000 into His Savings Account