A loan is repayable by decreasing quarterly instalments made in arrears for 8 years. The payment made at the end of the first quarter year is £2,100 and subsequent payments decrease by £20 each quarter. The instalments were calculated using a nominal rate of interest of 6% per annum convertible quarterly. Immediately after the 10th instalment has been made, it is agreed that the annual decrease will no longer occur. Thus, the future instalments will continue at the same level as in the 10th payment, for a shorter term, and with a smaller amended payment at the end of the loan contract. 1. Calculate the remaining revised term of the loan in whole quarter years. 2. Calculate, to 2 decimal places, the amount of the final amended instalment.

PLEASE, WRITE THE SOLUTIONS ON PAPER, EXPLAINING THE ENTIRE PROCESS, THE ONLY POSSIBLE SOLUTIONS ARE THE STIPULATED ONES

Please answer part dd and ee of C, strictly follow the formula.

Solve for the unknown interest rate in each of the following: (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Present Value $ 290 410 44,000 43,261 Years 3 18 20 Interest Rate % % % % Future Value $ 345 1,253 209,290 388,485

Complete the table by finding the balance A when $18,000 is invested at rate r for t years, compounded continuously. (Round your answers to two decimal places.) r = 8% t 10 20 30 40 50 A $ $ $ $ $

3. * The force of interest (t) at time t (measured in years) is a + bt² where a and b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5 and £230 at t = 10. 1 (a) Show that a = log (1.05) - 30 log(1.15) = 0.008352, and b = 250 log(1.15) - 125 log(1.05) = 0.0001687. (b) Compute A(0, 7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6, 7). What is the equivalent constant annual interest rate for the year from t = 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t = 0 to t = 10.