Final answer:
The effective interest rate of quarterly payments of $1,510 on a loan of $38,460 over 9 years can be determined using a financial calculator or software by inputting the respective values and solving for the interest rate.
Step-by-step explanation:
To find the effective interest rate for quarter-end payments of $1,510 to settle a loan of $38,460 in 9 years, one needs to set up an amortization problem taking into account the frequency of payments and the total number of payments made. In this scenario, there are 36 quarterly payments (9 years x 4 quarters per year). The effective interest rate can be found using financial calculators or software capable of solving for interest rates given a loan amount, payment amount, and number of payments.
Unfortunately, without access to such tools or additional formulas, I can't provide the precise effective interest rate here. However, using a financial calculator, one would input the present value (loan amount), the payment amount, the number of payments, and then solve for the interest rate. The effective interest rate would generally be higher than the nominal rate because interest compounds more frequently with quarterly payments than with annual payments.
The calculation would conceptualize the loan similarly to how a $1,000,000 loan over 30 years would be handled, where the total paid can exceed twice the loan amount, which highlights the impact of interest over time.