Help in solving the following questions.

Find the accumulated value of a payment stream of 0.3+1.5/ that is received continuously from time 4 to time 8 during which time the force of interest is 0.01+0.05 .A woman takes out a home improvement loan for f11,000 over 5 years. She makes monthly repayments in arrears and the bank charges an effective rate of interest of 6% pa. (i) What is the monthly repayment? [2] (ii) How much interest does she pay in the third year? [2] (iii) How much capital is repaid in the 20" instalment? [2] (iv) At the end of the fourth year she decides to make further improvements to her house and wants to borrow another $4,000 at that stage. If her total balance is to be repaid over 3 years by level monthly payments and there is no alteration to the interest rate, how much is each payment? [3] [Total 91A motor company runs tests to investigate the fuel consumption of cars using a newly developed fuel additive. Sixteen cars of the same make and age are used, eight with the new additive and eight as controls. The results, in miles per gallon over a test track under regulated conditions, are as follows: Control 27.0 32.2 30.4 28.0 26.5 25.5 29.6 27.2 Additive 31.4 29.9 33.2 34.4 32.0 28.7 26.1 30.3 Obtain a 95% confidence interval for the increase in miles per gallon achieved by cars with the additive. State clearly any assumptions required for this analysis