Answer:
11.74% ; 11.38%; 11.01%
Explanation:
Given the following :
Arithmetic return (Ar) = 11.9%
Geometric return (Gr) = 9.9%
N = 86 years = Past period
A) Return in the next 8 years
T = future period = 8 years
Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.
Return = (8 - 1) / (86 - 1) * 0.099 + (86 - 8) / (86 - 1) * 0.119
(0.0823529 * 0.099) + (0.9176470 * 0.119)
= 0.1173529301
= 0.1173529301 * 100 = 11.74%
B) over the next 23 years
T = 23 years
Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.
Return = (23 - 1) / (86 - 1) * 0.099 + (86 - 23) / (86 - 1) * 0.119
(0.2588235 * 0.099) + (0.7411764 * 0.119)
= 0.1138235181
= 0.1138235181 * 100 = 11.38%
C.) over 39 years
F = 39 years
Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.
Return = (39 - 1) / (86 - 1) * 0.099 + (86 - 39) / (86 - 1) * 0.119
(0.4470588 * 0.099) + (0.5529411 * 0.119)
= 0.1100588121
= 0.1100588121 * 100 = 11.01%
