Suppose $1,000 is compounded quarterly for 4 years. What rate is needed to reach a total of $2,000? Round to the nearest tenth of a percent.

Question

use
a=p(1+r/n)^nt

Answer 1

let the quarterly rate be i

1000(1 + i)^16 = 2000
(1+i)^16 = 2
take the 16th root of both sides

1+i = 2^(1/16)
1+i = 1.04427
i = .04427

the quarterly rate is 4.427 %
the annual rate compounded quarterly is 17.7%

(time to have that mathbook updated.
a 17% interest rate is a fantasy these days)