final answer for question (3): 2.81

question (4): 94.20

I just need the explanation

3. Kate is awarded a 10-year annuity-due making monthly payments of 50. Immediately after the 20th payment of the annuity, it is exchanged for a perpetuity-due whose first monthly payment is K and each subsequent monthly payment increases by 1.15%. Using an annual nominal rate of interest of 15% convertible monthly, calculate K. 4. = Riley makes deposits into an account at a continuous rate of pe = b(12+t). where b is a constant. She makes these deposits from time t = 0 to time t = 6. This account credits the following force of interest: 8 2 12 + + fort >0. If the present value of her deposits is 5,500, calculate b. 3. Kate is awarded a 10-year annuity-due making monthly payments of 50. Immediately after the 20th payment of the annuity, it is exchanged for a perpetuity-due whose first monthly payment is K and each subsequent monthly payment increases by 1.15%. Using an annual nominal rate of interest of 15% convertible monthly, calculate K. 4. = Riley makes deposits into an account at a continuous rate of pe = b(12+t). where b is a constant. She makes these deposits from time t = 0 to time t = 6. This account credits the following force of interest: 8 2 12 + + fort >0. If the present value of her deposits is 5,500, calculate b