The value of n which I will use is 32 in the given formula of ordinary annuity.
We know that formula for ordinary annuity is
FV = [tex]\frac{P[ (1+ \frac{r}{m})^m^T-1]}{\frac{r}{m} }[/tex]
where FV is future value, P is present value, r is interest rate, T is number of years, m is number of periods based on compounding frequently.
In the given problem r%= 12%
⇒ r = 0.12
⇒ T = 8 years
⇒ m = compounded quarterly
⇒ m = 4
⇒ mT = 8×4= 32
Given ordinary annuity formula is
[tex]S= R[ \frac{(1+i)^n - 1}{i}][/tex]
where i = r/m = 0.12/4 which is 0.03
⇒ n = mT = 8×4 =32
Hence, the value of n used will be 32.
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