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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.18 : An investor is planning to purchase a small office for biochemical engineering consultancy on loan. In the calculation of the discount of payment in arrears, the following formula is used : y = 1 / (1 + r) ^ 1 + 1 / (1 + r) ^ 2 + 1 / (1 + r) ^ 3 + ... + 1 / (1 + r) ^ n where y = present value, r = interest rate of discount, n = number of payment, ^ = power used in certain computer languages for mathematics. (a) What is the meaning of : arrears? (b) Find a mathematical equation of y (1 + r). (c) Calculate, in less than 3 terms, y as a function of r and n.
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Answer Posted / kangchuentat
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.18 : (a) Backward. (b) Let Equation 1 : y = 1 / (1 + r) ^ 1 + 1 / (1 + r) ^ 2 + ... + 1 / (1 + r) ^ n. Multiply Equation 1 with (1 + r) will produce Equation 2 : y (1 + r) = 1 + 1 / (1 + r) ^ 1 + ... + 1 / (1 + r) ^ (n - 1). (c) Equation 2 - Equation 1 will produce yr = 1 - 1 / (1 + r) ^ n, then y = [ 1 - 1 / (1 + r) ^ n ] / r. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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