Questions: Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate. Quarterly payments of 1000 are made for 11 years to repay a loan at 9.2% compounded quarterly. i= (Type an integer or a decimal.)

Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate. Quarterly payments of 1000 are made for 11 years to repay a loan at 9.2% compounded quarterly. i= (Type an integer or a decimal.)
Transcript text: Find $i$ (the rate per period) and $\mathbf{n}$ (the number of periods) for the following loan at the given annual rate. Quarterly payments of $\$ 1000$ are made for 11 years to repay a loan at $9.2 \%$ compounded quarterly. $\mathrm{i}=$ $\square$ (Type an integer or a decimal.)
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Solution

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Solution Steps

Step 1: Calculate the Rate per Period ($i$)

To find the rate per period, we divide the annual interest rate by the compounding frequency. Given an annual interest rate of 9.2% and a compounding frequency of 4 times per year, the rate per period is calculated as follows: \[ i = \frac{0.092}{4} = 0.023 \]

Step 2: Calculate the Number of Periods ($n$)

The number of periods is found by multiplying the loan term in years by the compounding frequency. With a loan term of 11 years and a compounding frequency of 4, the number of periods is: \[ n = 11 \times 4 = 44 \]

Final Answer:

The rate per period ($i$) is 0.023, and the number of periods ($n$) is 44.

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