Math  /  Algebra

QuestionFind i (the rate per period) and n (the number of periods) for the following loan at the given annual rate. Semiannual payments of $4,400\$ 4,400 are made for 11 years to repay a loan at 8.1%8.1 \% compounded semiannually. i=i= \square (Type an integer or decimal rounded to four decimal places as needed.)

Studdy Solution

STEP 1

1. The loan has semiannual payments.
2. The annual interest rate is 8.1%8.1\%.
3. The interest is compounded semiannually.
4. Payments are made over a period of 11 years.
5. We need to find the rate per period (ii) and the number of periods (nn).

STEP 2

1. Calculate the rate per period (ii).
2. Calculate the number of periods (nn).

STEP 3

Calculate the rate per period (ii).
Since the interest is compounded semiannually, we need to divide the annual interest rate by the number of compounding periods per year. The annual rate is 8.1%8.1\%, which is 0.0810.081 as a decimal.
i=0.0812 i = \frac{0.081}{2}

STEP 4

Perform the division to find ii.
i=0.0812=0.0405 i = \frac{0.081}{2} = 0.0405
Thus, the rate per period is 0.04050.0405.

STEP 5

Calculate the number of periods (nn).
Since payments are made semiannually for 11 years, we multiply the number of years by the number of periods per year.
n=11×2 n = 11 \times 2

STEP 6

Perform the multiplication to find nn.
n=11×2=22 n = 11 \times 2 = 22
Thus, the number of periods is 2222.
The rate per period is i=0.0405i = 0.0405 and the number of periods is n=22n = 22.

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