Find i (the rate per period) and n (the number of periods) for the annuity.
-Semiannual deposits of $400 are made for 10 years into an annuity that pays 7% compounded semiannually.
A) i = 0.07; n = 10
B) i = 0.035; n = 20
C) i = 0.35; n = 10
D) i = 0.0175; n = 40

Question

Quizplus · Accepted Answer

The interest rate (i) in the question is given as an annual rate, compounded semiannually. So we need to divide the annual rate by 2 to get the semiannual rate. Therefore, i = 0.07/2 = 0.035. The number of periods (n) is given as 10 years, but since deposits are made semiannually, we need to multiply by 2 to get the total number of deposit periods. Therefore, n = 10 * 2 = 20. Choice B matches these values. The interest rate per period is half of the annual interest rate as interest is compounded semiannually. So, the interest rate per period is (7%/2) = 3.5%. The number of periods is the total number of semiannual deposits made, which is (10 years) x (2 semiannual deposits per year) = 20 semiannual deposits. Therefore, the correct choice is B, with i = 0.035 and n = 20.

Find I (The Rate Per Period) and N (The Number