Final answer:
The original value of the loan is $2,826.39 and the total interest that Tom has to pay is $773.61.
Step-by-step explanation:
To find the original value of the loan, we can use the formula for the present value of an annuity:
Present Value = Payment ／ [(1 - (1 + interest rate)^(-number of payments)) / interest rate]
Plugging in the given values, we have:
150 = X ／ [(1 - (1 + 0.12/12)^(-2*12)) / (0.12/12)]
Solving for X, we get:
X = $2,826.39
Therefore, the original value of the loan is $2,826.39.
To find the total interest, we can subtract the original loan amount from the total payments made over two years:
Total Interest = Total Payments - Original Loan Amount
Total Payments = 150 * 2 * 12 = $3,600
Therefore, the total interest that Tom has to pay is $3,600 - $2,826.39 = $773.61.