$20,000 for 14 years compounded at 8% semiannually results in how many periods?
A)64
B)28
C)12
D)14
E)None of these

Question

Quizplus · Accepted Answer

The formula for compound interest is:
A = P(1 + r/n)^(nt)
A: final amount 
P: principal 
r: annual interest rate 
n: number of times the interest is compounded per year 
t: time in years

Here, P = $20,000, r = 8%, n = 2 (semiannually compounded), t = 14 years

We need to find the number of periods (semiannual) which we can do by rearranging the formula: 
t = log(A/P) / log(1 + r/n)^(1/n)
t = log($20,000 x (1 + 0.08/2)^(2x14)) / log(1 + 0.08/2)^(1/2) 
t = 28

So, the answer is choice B) 28.

$20,000 for 14 Years Compounded at 8% Semiannually Results in How