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An amortized loan has 10 annual payments at the end of each year starting one year from now. The first 5 payments are $1000 each and the final 5 payments are $500 each. Interest is at an ef- fective annual rate of 10%. Find each of the following: (i) the initial loan amount (ii) the outstanding balance just after the 3rd payment (iii) the interest and principal in the 4th payment (iv) the outstanding balance just after the 8th payment