Final answer:
Jason will make semi-annual payments of approximately $3,331.17. The total cash repayment for the loan over the 5-year period is $33,311.70. Jason will have paid $3,311.70 in interest on the loan.
Step-by-step explanation:
To calculate the semi-annual payments, we can use the formula for the present value of an annuity. In this case, the loan amount is $30,000, the interest rate is 4% compounded semi-annually, and the loan period is 5 years (10 semi-annual periods).
The formula for the present value of an annuity is:
PV = PMT x (1 - (1 + r)^(-n)) / r
Where PV is the present value of the annuity, PMT is the payment made at each period, r is the interest rate per period, and n is the number of periods.
Plugging in the values:
PV = $30,000, r = 4% / 2 = 0.02, and n = 5 x 2 = 10.
By rearranging the formula, we can solve for PMT:
PMT = PV x (r / (1 - (1 + r)^(-n)))
Using the values above, we get:
PMT = $30,000 x (0.02 / (1 - (1 + 0.02)^(-10))) ≈ $3,331.17
Therefore, Jason will make semi-annual payments of approximately $3,331.17.
The total cash repayment for the loan over the 5-year period can be calculated by multiplying the semi-annual payment by the number of periods:
Total Cash Repayment = $3,331.17 x 10 = $33,311.70.
The interest paid on the loan can be calculated by subtracting the loan amount from the total cash repayment:
Total Interest = Total Cash Repayment - Loan Amount = $33,311.70 - $30,000 = $3,311.70.