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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

Respuesta :

Answer:

8

Step-by-step explanation:

Given:

Annuity at time (n + 1) = 13.776

(1 + i)ⁿ = 2.476

Now,

[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]

or

d = 0.1071

therefore,

d = [tex]\frac{i}{1+i}[/tex]

or

0.1071 = [tex]\frac{i}{1+i}[/tex]

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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