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प्रश्न
Solve the following :
A person purchases a television by paying ₹20,000 in cash and promising to pay ₹1,000 at end of every month for the next 2 years. If money is worth 12% p. a. converted monthly, find the cash price of the television. [(1.01)–24 = 0.7875]
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उत्तर
Person buys the television for ₹20,000 in cash.
∴ First payment = ₹20,000
Remaining value of the television was paid in monthly instalments of ₹1,000.
∴ C= ₹1,000,
The duration of monthly installments is of 2 years.
∴ n = 24
Rate of interest is 12% p.a.
∴ r = `(12)/(12)` = 1% p.m.
∴ i = `"r"/(100) = (1)/(100)` = 0.01
The amount is paid at the end of every month.
∴ It is an immediate annuity.
Now, to find sum of all instalments we have to find present value.
∴ P = `"C"/"i"[1 - (1 + "i")^-"n"]`
∴ P = `(1,000)/(0.01)[1 - (1 + 0.01)^24]`
= 1,00,000 [1 – (1.01)–24]
= 1,00,000 (1 – 0.7875)
= 1,00,000 x 0.2125
∴ P = ₹21,250
∴ Cash price of the television = First Payment + Present Value
= 20,000 + 21,250
= ₹41,250
∴ Cash price of the television is ₹41,250.
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The future amount, A = ₹ 10,00,000
Period, n = 20, r = 5%, (1.025)20 = 1.675
A = `"C"/"I" [(1 + "i")^"n" - 1]`
I = `5/200` = `square` as interest is calculated semi-annually
A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`
= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
