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 va lue 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
1 answer:
Answer:
8
Step-by-step explanation:
Given:
Annuity at time (n + 1) = 13.776
(1 + i)ⁿ = 2.476
Now,
here, d =
thus,
or
d = 0.1071
therefore,
d =
or
0.1071 =
or
0.1071 + 0.1071i = i
or
i = 0.1199
now,
(1 + i)ⁿ = 2.476
or
(1 + 0.1199)ⁿ = 2.476
1.1199ⁿ = 2.476
taking log both sides
n × log(1.1199) = log(2.476)
or
n = 8.006 ≈ 8
hence,
the answer is 8
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