Loan and annuity (prospective methods) The question is a loan of $10,000 is to be repaid over 10 years by level annual repayment of capital and interest. The interest rate to be charged on the capital outstanding will be 6% per annum for the first 4 years and 8% per annum thereafter i)How much of the loan is outstanding at the beginning of the 3rd Year. I have already know the answer is $8345.53. But i got the wrong answer (8107.66) when i using the prospective methods. So i am so confuse about which part am i wrong in the prospective methods. Thank you so much. !enter image description here

You made a mistake on your third line. It should be

$$v^2_{0.06}a_{\overline{6|}0.08}+a_{\overline{2|}0.06}$$