This unit applies time value of money to:
Compounding factor: (1 + i)^n Discount factor: 1/(1 + i)^n
Here i = rate per period (decimal), n = number of periods.
An annuity is a series of equal payments/receipts at equal intervals.
Types:
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Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
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This unit applies time value of money to:
Compounding factor: (1 + i)^n Discount factor: 1/(1 + i)^n
Here i = rate per period (decimal), n = number of periods.
An annuity is a series of equal payments/receipts at equal intervals.
Types:
FV (ordinary annuity) = R × [((1+i)^n − 1)/i]
PV (ordinary annuity) = R × [1 − 1/(1+i)^n] / i
FV (annuity due) = FV (ordinary) × (1 + i) PV (annuity due) = PV (ordinary) × (1 + i)
EMI is a fixed monthly instalment consisting of interest + principal repayment.
EMI = P × [ i(1+i)^n ] / [ (1+i)^n − 1 ]
Sinking fund is equal deposits to accumulate a target sum.
S = R × [((1+i)^n − 1)/i] so R = S / [((1+i)^n − 1)/i]
SLM depreciation per year = (Cost − Scrap)/Life
WDV book value after n years = Cost × (1 − r)^n
From this topic
Ordinary annuity: payments occur at the end of each period; annuity due: payments occur at the beginning.
Annuity due gives one extra period of interest on each payment, so its PV and FV are higher than ordinary annuity.
Examples: Ordinary—loan instalment at month end; Due—rent paid at start of month.
R = 2,000, i = 0.10, n = 3. FV = R × [((1+i)^n − 1)/i] = 2,000 × [((1.10)^3 − 1)/0.10] (1.10)^3 = 1.331 Factor = (1.331 − 1)/0.10 = 3.31 FV = 2,000 × 3.31 = ₹6,620 (approx).
A sinking fund is a method of accumulating a target amount by making equal periodic deposits that earn interest. It is commonly used for replacement of assets or repayment of loans/debentures.
If deposit each period is R, rate per period is i, and number of periods is n, the accumulated amount is: S = R × [((1+i)^n − 1)/i] So required deposit: R = S / [((1+i)^n − 1)/i]
Example: To accumulate ₹1,00,000 in 5 years at 10% p.a. with annual deposits: Factor = ((1.10)^5 − 1)/0.10 = (1.61051 − 1)/0.10 = 6.1051 R = 1,00,000/6.1051 ≈ ₹16,380 (approx).
Thus, equal deposits plus interest create the future fund.