Question
Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate.
Semiannual payments of $3 comma 000 are made for 17 years to repay a loan at 5.2% compounded semiannually.
Semiannual payments of $3 comma 000 are made for 17 years to repay a loan at 5.2% compounded semiannually.
Answers
GPT-4o mini
To determine the interest rate per period (\(i\)) and the number of periods (\(n\)) for the loan, we can follow these steps:
1. **Identify the Annual Interest Rate:** The annual interest rate given is 5.2%.
2. **Calculate the Semiannual Interest Rate (\(i\)):** Since the interest is compounded semiannually, we will divide the annual rate by 2:
\[
i = \frac{5.2\%}{2} = \frac{0.052}{2} = 0.026 \quad \text{(or 2.6% per semiannual period)}
\]
3. **Determine the Number of Semiannual Periods (\(n\)):** The loan is to be repaid over 17 years with semiannual payments.
\[
n = 17 \text{ years} \times 2 \text{ periods per year} = 34 \text{ periods}
\]
### Summary:
- **Rate per period (i):** 0.026 (or 2.6%)
- **Number of periods (n):** 34 periods
With these calculations, you can proceed to analyze or utilize this information further concerning the loan.
1. **Identify the Annual Interest Rate:** The annual interest rate given is 5.2%.
2. **Calculate the Semiannual Interest Rate (\(i\)):** Since the interest is compounded semiannually, we will divide the annual rate by 2:
\[
i = \frac{5.2\%}{2} = \frac{0.052}{2} = 0.026 \quad \text{(or 2.6% per semiannual period)}
\]
3. **Determine the Number of Semiannual Periods (\(n\)):** The loan is to be repaid over 17 years with semiannual payments.
\[
n = 17 \text{ years} \times 2 \text{ periods per year} = 34 \text{ periods}
\]
### Summary:
- **Rate per period (i):** 0.026 (or 2.6%)
- **Number of periods (n):** 34 periods
With these calculations, you can proceed to analyze or utilize this information further concerning the loan.