Here is the information from 22:

Not sure which information from 22 is necessary to solve 23. Please show all steps.

23. Assume that the homebuyer of Exercise 22 elects to repay the loan continuously at the rate of a M dollars per month, where a is a constant greater than l(This is called accelented payment.) (a) Determine the time T(a) when the loan will be paid off and the amount S(o) that the home- buyer will save. Suppose P.-850.000, r8%, and N-15. Compute the savings realized by accelerated payments with a (b) 1.05,1.10, and 1.15. 22. A homebuyer borrows Po dollars at an annual interest rate r, agreeing to repay the loan with equal monthly payments of M dollars per month over N years. (a) Derive a differential equation for the loan principal (amount that the homebuyer owes) P(t) at time t > 0, making the simplifying assumption that the homebuyer repays the loan con- tinuously rather than in discrete steps. (See Example 4.1.6 (b) Solve the equation derived in (a). (c) Use the result of (b) to determine an approximate value for M assuming that each year has exactly 12 months of equal length. It can be shown that the exact value of M is given by (d) 121-(1+/12)-12)-1 Compare the value of M obtained from the answer in (c) to the exact value if i) Po $50. 000, r = 7+%, N = 20 (ii) P,-$150. 000, r = 9.0%, N = 30. 23. Assume that the homebuyer of Exercise 22 elects to repay the loan continuously at the rate of a M dollars per month, where a is a constant greater than l(This is called accelented payment.) (a) Determine the time T(a) when the loan will be paid off and the amount S(o) that the home- buyer will save. Suppose P.-850.000, r8%, and N-15. Compute the savings realized by accelerated payments with a (b) 1.05,1.10, and 1.15. 22. A homebuyer borrows Po dollars at an annual interest rate r, agreeing to repay the loan with equal monthly payments of M dollars per month over N years. (a) Derive a differential equation for the loan principal (amount that the homebuyer owes) P(t) at time t > 0, making the simplifying assumption that the homebuyer repays the loan con- tinuously rather than in discrete steps. (See Example 4.1.6 (b) Solve the equation derived in (a). (c) Use the result of (b) to determine an approximate value for M assuming that each year has exactly 12 months of equal length. It can be shown that the exact value of M is given by (d) 121-(1+/12)-12)-1 Compare the value of M obtained from the answer in (c) to the exact value if i) Po $50. 000, r = 7+%, N = 20 (ii) P,-$150. 000, r = 9.0%, N = 30