Answer: The amount borrowed for the loan is approximately $9,116.48.
Step-by-step explanation:
we can use the formula for calculating the present value of an ordinary annuity:
PV = R * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value or the amount borrowed.
R is the periodic payment.
r is the interest rate per period.
n is the number of periods.
In this case, R is $694.60, the interest rate is 5.8% (or 0.058 as a decimal), and the payments are made semiannually for 7 years (or 7 * 2 = 14 periods).
Plugging in the values into the formula:
PV = $694.60 * (1 - (1 + 0.058)^(-14)) / 0.058
Calculating this expression gives us:
PV ≈ $694.60 * (1 - 0.231055) / 0.058
PV ≈ $694.60 * 0.768945 / 0.058
PV ≈ $9,116.48
Therefore, the amount borrowed for the loan is approximately $9,116.48.