Final answer:
To calculate the original loan amount borrowed based on quarterly payments, the present value formula for annuities is used, taking into account the quarterly interest rate and the total number of payments. Financial calculators or spreadsheets can assist in the computation.
Step-by-step explanation:
The question pertains to the calculation of the original loan amount based on quarterly payments made on the loan with a given interest rate and time frame. We can solve it using the formula for the present value of an annuity because the payments are made at regular intervals and are of equal amounts.
The formula to find the present value (PV) of an annuity is PV = Pmt x [(1 - (1 + r)^-n) / r], where Pmt is the payment amount per period, r is the interest rate per period, and n is the total number of payments.
Since the payments are quarterly and the interest is annual, we need to adjust the interest rate and the number of payments accordingly:
- Quarterly interest rate (r) = (12% annual rate) / 4 = 3% = 0.03 per quarter
- Total number of payments (n) = (24 months) / 3 months per quarter = 8 quarters
- Quarterly payment (Pmt) = $733.88
Plugging these into the formula gives us:
PV = $733.88 x [(1 - (1 + 0.03)^-8) / 0.03]
Calculating this yields the original loan amount borrowed. You can use financial calculators or spreadsheets like Excel to compute this value easily.