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+0.05t A woman takes out a home improvement loan for 11,000 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? (ii) How much interest does she pay in the third year? (iii) How much capital is repaid in the 20th instalment? (iv) [2] [2] [2] 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 9] A 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 Additive 27.0 32.2 30.4 28.0 26.5 25.5 29.6 27.2 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.