Questions: Find i (the rate per period) and n (the number of periods) for the following annuity. Semiannual deposits of 1,500 are made for 10 years into an annuity that pays 7.3% compounded semiannually. i= (Type an integer or a decimal.) n=

Find i (the rate per period) and n (the number of periods) for the following annuity. Semiannual deposits of 1,500 are made for 10 years into an annuity that pays 7.3% compounded semiannually. i= (Type an integer or a decimal.) n=
Transcript text: Find i (the rate per period) and n (the number of periods) for the following annuity. Semiannual deposits of $\$ 1,500$ are made for 10 years into an annuity that pays $7.3 \%$ compounded semiannually. $i=$ $\square$ (Type an integer or a decimal.) \[ \mathrm{n}= \] $\square$
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Solution

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Solution Steps

To solve this problem, we need to determine the rate per period (i) and the number of periods (n) for the given annuity. Since the annuity is compounded semiannually, we will adjust the annual interest rate and the number of years accordingly.

  1. Rate per period (i): The annual interest rate is 7.3%. Since the compounding is semiannual, we divide the annual rate by 2 to get the rate per period.

  2. Number of periods (n): The annuity lasts for 10 years, and since deposits are made semiannually, we multiply the number of years by 2 to get the total number of periods.

Step 1: Calculate the Rate per Period

The annual interest rate is given as \( 7.3\% \). Since the compounding is semiannual, we divide this rate by 2 to find the rate per period:

\[ i = \frac{7.3}{2} \times \frac{1}{100} = 0.0365 \]

Step 2: Calculate the Number of Periods

The annuity lasts for 10 years, and since deposits are made semiannually, we multiply the number of years by 2 to find the total number of periods:

\[ n = 10 \times 2 = 20 \]

Final Answer

The values are: \[ i = 0.0365 \] \[ n = 20 \]

Thus, the final answers are: \[ \boxed{i = 0.0365} \] \[ \boxed{n = 20} \]

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