A number of credit tranches Rt - 31 August 2012

A number of credit tranches Rt produced after the time nt. The total period of payments is n years. Required to determine the accrued at the end of the term the amount of debt, if interest accrued at the rate of complex i. In this case, nara ¬ sorbed amount is determined by the following formula:

S = ΣRt (l + i) n-nt, where
Rt - size t-go tranche;
i - interest rate;
nt - the number of years from the year of issuance of the first tranche;
n - the time that is determined by the amount of the debt.
Next, you must determine the amount of indebtedness of the peasant farm to the cooperative "Agrocredit" at the beginning of 2010. at an interest rate i = 16%. In this case, the cooperative has developed the following schedule issuing loans:
July 1, 2006. - 50 thousand
January 1, 2007. - 150 thousand
January 1, 2009. - 180 thousand
The amount owed to the cooperative farm "Agrocredit" at the beginning of 2010. will be:
S = 50 * (1 + 0.16) 4-0,5 + 150 * (1 + 0.16) 4-1 + 180 * (1 + 0.16) 4-3 = 62.5 + 234.0 + 208.8 = 505.3 thousand
Such a way of repaying the debt, namely parts called debt amortization.
Debt of the borrower to the credit cooperative "Agrocredit" can be repaid in equal installments over several years. Then the sum of each year going to repay the amount to:
d =, where
d - the amount going to pay off;
D - the principal amount;
n - number of years of repayment.
The size of the debt will be reduced each year. If in the first year of the amount of debt is D, then the second year it is D - d, in the third year - D - 2d etc. If we consider that the interest is paid once at the end of the year at the rate g, then for the first and subsequent years, the amount of interest equal to Dg, (D - d) g, (D - 2d) g, etc.
Urgent payment at the end of the first year consists of the principal - d and interest - Dg:
Yt = Dg + d
At the end of year t-urgent payment Yt is:
Yt = Dt * g + d, t = 1, 2, .... n, where
Dt - the stock of debt at end of year t,
g - the interest rate.
For example, debt SEC them. Lenin 400 thousand to pay equal installments over 4 years postnumerando payments (payments made at the end of the rent). The loan was issued at 18% per annum. Need to determine what will be the sum ¬ hedgehog suitable borrowing costs and the ratio of the amounts of interest and principal repayment.