Final answer:
The annual installments are approximately $7,240.18 To calculate the annual installments for a loan, we can use the formula for the present value of payments.
Step-by-step explanation:
To compute the annual installments for a $30,000 loan with an 8% interest rate applied to the remaining balance, the formula for the present value of payments can be employed. The present value (PV) is determined by multiplying the annual installment (R) by the present value interest factor of an annuity (1−(1 + i)¯n), where i represents the interest rate per period, and n is the number of periods.
In this scenario, the loan requires repayment through six annual installments (n = 6), and the interest rate is 8% (i = 0.08). By substituting these values into the formula, the calculation yields the annual installment amount necessary to fulfill the loan obligation over the specified duration.
PV = R × (1−(1 + 0.08)⁻⁶)
Now we need to solve for R:
R = PV ÷ (1−(1 + 0.08)⁻⁶)
Plugging in the values:
R = $30,000 ÷ (1−1.08⁶)
R ≈ $7,240.18