On October 1, 2022 you take out a loan of $20000 from the bank, which offers a promotional rate of 3% (APR) compounded monthly. You agree to make monthly payments of R for 3 years at the end of each month, starting October 31, 2022, so that the last payment is made on September 30, 2025.

(a) Compute R (rounded to two decimal places).

(b) Using your answer in part (a), compute how much principal remains on the loan on June 1, 2023.

(c) On June 1, 2023 the promotional rate ends, and the new rate for the loan becomes 10% (APR), compounded monthly. Compute your new monthly payments S starting June 30, 2023, assuming that you still fully pay off the loan on September 30, 2025.

(d) The bank offers you another option: you can keep the monthly payments unchanged (so the same as R in part (a)) after the interest rate increase on June 1, 2023. Instead, the amortization period will be extended past the original three years. Determine when the loan will be paid off.