Based on the available information, Prateek would need to pay approximately $14,149.50 to settle the debt at the end of 3 years.
To calculate the amount required to settle the debt at the end of 3 years, use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (amount required to settle the debt)
P = Principal amount (initial debt)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
Let's calculate the amount required to settle the debt for each note separately:
For the first note:
Principal amount (P1) = $2800
Number of years (t1) = 3
Annual interest rate (r) = 13.25% = 0.1325 (in decimal form)
Number of compounding periods per year (n) = 4 (quarterly compounding)
A1 = P1(1 + r/n)^(nt)
A1 = $2800(1 + 0.1325/4)^(4*3)
A1 ≈ $2800(1 + 0.033125)^12
A1 ≈ $2800(1.033125)^12
A1 ≈ $2800(1.443619)
A1 ≈ $4044.17
For the second note:
Principal amount (P2) = $7000
Number of years (t2) = 3
Annual interest rate (r) = 13.25% = 0.1325 (in decimal form)
Number of compounding periods per year (n) = 4 (quarterly compounding)
A2 = P2(1 + r/n)^(nt)
A2 = $7000(1 + 0.1325/4)^(4*3)
A2 ≈ $7000(1 + 0.033125)^12
A2 ≈ $7000(1.033125)^12
A2 ≈ $7000(1.443619)
A2 ≈ $10,105.33
To settle the debt at the end of 3 years, Prateek would need to pay a total of A1 + A2:
Total amount required = A1 + A2
Total amount required ≈ $4044.17 + $10,105.33
Total amount required ≈ $14,149.50
Therefore, Prateek would need to pay approximately $14,149.50 to settle the debt at the end of 3 years.