SOLUTION: A man borrowed sum of $3600 to be redeemed in 40 installments which made an Arithmetic Progression. After paying 30 installments he died leaving behind a sum of $1200 unpaid. His h
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Question 494799: A man borrowed sum of $3600 to be redeemed in 40 installments which made an Arithmetic Progression. After paying 30 installments he died leaving behind a sum of $1200 unpaid. His heirs accepted to pay his remaining liability. What was the first installment paid by (1) The Man (2) His Heirs.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
looks like he paid 80 dollars each installment.
looks like his heirs paid 120 dollars each installment.
he borrowed 3600.
he paid 30 installments and then died leaving 1200 unpaid.
this means he paid 2400 in 30 installments which equals 80 dollars per installment.
1200 was left with 10 installments to go.
this means that his heirs had to pay 120 per installment for 10 installments.
making this into an arithmetic progression is a little tricky, but here's how i would do it.
An = A1 + (n-1)d
this means that the last term in the progression is equal to the first term in the progression plus the difference times the number of terms in the progression minus 1.
the man paid 30 installments, so the number of terms in his progression was 31.
this includes the first term plus the 30 terms of payments.
the first term in his progression was 3600
the last term in his progression was 1200
n = 31
An = A1 + (n-1)d becomes:
1200 = 3600 + 30d
subtract 3600 from both sides of this equation to get:
-2400 = 30d
divide both sides of this equation by 30 to get:
-80 = d
the common difference is -80 which is what he paid for each installment.
the heirs were left with 1200 to pay.
they had to pay it in 10 installments.
n is equal to 11 for them.
this is the first term plus the 10 terms of repayment.
An = 0 (after all the remaining payments have been paid).
A1 = 1200
n = 11
An = A1 + (n-1)d becomes:
0 = 1200 + 10d
subtract 1200 from both sides of this equation to get:
-1200 = 10d
divide both sides of this equation by 10 to get:
d = -120
the man paid 80 dollars per installment.
his heirs paid 120 dollars per remaining installment.
that's the way i see it.
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