You took the interest of just the annual payment (800,000), and not of the entire remaining principal. The accrued interest is the interest that has accumulated since the principal investment OR the last interest payment (in this case, the interest paid on October 1, 2006).
So, the remaining principal after the first payment is 1,600,000 (2,400,000 - 800,00). Accrued interest is equal to the fraction of the year (9 months have passed since the last interest payment, so 9/12 = 3/4) multiplied by the remaining principal (1,600,000) multiplied by the interest rate (10%, so .1).
(3/4)*(1,600,000)*(.1) = 120,000.
You use the remaining principal amount because that is what is gaining interest in those 9 months, not just the 800,000 installment Allen Corp is due to pay.
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