Answer:
(B) 6.25%
Explanation:
January 1, 1997 = $100,000
April 1. 1997 = $103,000 - $8,000 = $95,000
January 1, 1999 = $103,992
annual interest rate for 1997 = i = (x - 100,000 + 8,000) / [100,000 - 8,000(1 - ³/₁₂) = (x - 100,000 + 8,000) / [100,000 - 8,000(1 - 0.25) = (x - 92,000) / 94,000
x = 92,000 + 94,000i
annual interest rate for 1998 = 1 + i = 103,992/x
x = 103,992/(1 + i)
0 = x(1 + i) - 103,992
now we replace x by 92,000 + 94,000i
0 = (92,000 + 94,000i)(1 + i) - 103,992
0 = (94,000 (1 + i) - 2,000)(1 + i) - 103,992
we now replace 1 + i by Y
0 = (94,000Y - 2,000)Y - 103,992
0 = 94,000Y² - 2,000Y - 103,992
using a calculator, Y = 6.25%
