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Mugdho
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Mugdho
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Mugdho
A man buys a scooter on making a cash down payment of $ 16224 and promises to pay two more yearly installments of equivalent amount in next two years. If the rate of interest is 4% per annum, compounded yearly, the cash value of the scooter, is:

A) $40000

B) $46824

C) $46000

D) $50000

Posted from my mobile device
We have been asked for the actual price of the scooter without the interest

Price of scooter = Down Payment + Principal of the 1st yr inst. + Principal of the 2nd yr inst.

\(A=P(1+r)^t\)
\(P=\frac{A}{(1+r)^t}\)

Installment 1 (paid at the end of Year 1):
\(P1= \frac{16224}{(1+0.04)^1} \)
P1=15600

Installment 2 (paid at the end of Year 2):
\(P2=\frac{16224}{(1+0.04)^2}\)
P2=15000

Price of scooter = 16224+15600+15000
= 46824

Option B
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KabyaS
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this is how I did it : if the man paid three equal instalments then the total amount paid is 16227*3. This should be equal to the sum of the cash value(x) of the scooter and the interest.
16227*3=x+4/100x+4/100(x+4/100x). Solving this will return the value of x.
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