Financial Mathematics

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A perpetuity is an annuity where payments continue forever. The present value of a perpetuity of ₹R payable at the end of each period is: P = R/i, where R = size of each payment and i = rate per perio

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Given: R = ₹500, i = 0.08/4 = 0.02 Present value P = R/i = 500/0.02 = ₹25,000

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A sinking fund is a fund established by setting aside revenue over time to fund a future capital expense or repay long-term debt. It differs from a savings account as it's set up for a particular purp

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R = A/S_{n|i}, where S_{n|i} = [(1 + i)ⁿ - 1]/i Where: R = Size of each payment, A = Amount to be accumulated, i = rate per period, n = number of payments

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A bond is characterized by: (1) Face Value/Par Value - price at issue and redemption, (2) Redemption Price - amount paid at maturity, (3) Discount/Premium - market price relative to face value, (4) No

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Bond Value (V) = R[1-(1+i)⁻ⁿ]/i + C(1+i)⁻ⁿ Where: V = bond value/purchase price, R = periodic dividend payment, C = redemption price, i = yield rate per period, n = number of periods

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Given: Face value = ₹1,000, Coupon rate = 10%, Yield = 8%, n = 5 years R = 1000 × 0.10 = ₹100 V = 100[1-(1.08)⁻⁵]/0.08 + 1000(1.08)⁻⁵ V = 100(3.9927) + 1000(0.6806) = 399.27 + 680.58 = ₹1,079.85

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EMI (Equated Monthly Instalment) is a monthly payment towards a loan at a fixed date every month. Two calculation methods: (1) Flat Rate Method: EMI = (P+I)/n, where interest is calculated on original