MATH SOLVE

4 months ago

Q:
# S (SOA) An annuity pays 1 at then end of each year for n years. Using an annual effective interest rate of i, the accumulated value of the annuity at time (n + 1) is 13.776. It is also known that (1 + i)* = 2.476. Calculate n. A) 4 B) 5 C) 6 D) 7 8

Accepted Solution

A:

Answer:8Step-by-step explanation:Given:Annuity at time (n + 1) = 13.776(1 + i)ⁿ = 2.476Now,[tex]S_{n/i}=\frac{(1+i)^n-1}{d}[/tex]here, d = [tex]\frac{i}{1-i}[/tex]thus,[tex]13.776=\frac{2.476-1}{d}[/tex]ord = 0.1071 therefore, d = [tex]\frac{i}{1+i}[/tex]or0.1071 = [tex]\frac{i}{1+i}[/tex]or0.1071 + 0.1071i = i ori = 0.1199 now,(1 + i)ⁿ = 2.476or(1 + 0.1199)ⁿ = 2.4761.1199ⁿ = 2.476taking log both sidesn × log(1.1199) = log(2.476)orn = 8.006 ≈ 8hence, the answer is 8