A sum of Rs. 13,390 was borrowed at 8% per annum compound interest and paid back in 2 years in two equal annual installments. What was the amount of each installment (approximately)?
Answers
Gɪᴠᴇɴ :-
- Principal = Rs.13,390 .
- Rate = 8% .
- Time = 2 Years.
Tᴏ Fɪɴᴅ :-
- What was the amount of each installment (approximately) ?
Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-
installment :- An equated yearly installment is a fixed payment amount made by a borrower to a lender at a specified date each calendar year.
Sᴏʟᴜᴛɪᴏɴ :-
Lets Try to Solve with Fractional method first to save Time.
Rate = 8% = (8/100) = (2/25)
in 1st Year :- 25(P) ---------------------- 27(installment)
in 2nd Year :- 25²(P) ------------------ 27²(installment)
Now, to Make installment Same :-
→ 27[[25 ----------------------- 27*27]
→ 1[ 625 ----------------------- 729]
That is Equal to :-
→ 675(P) --------------- 729 (installment)
→ 625(P) ----------------- 729 (installment)
So,
→ Total P = 675 + 625 = Rs.1300 .
Therefore, we can conclude That,
→ when P is 1300, our installment is = 729
→ when P is 1, our installment is = (729/1300)
→ when P is 13,390, our installment is = (729*13390)/1300 = Rs.7508.7 ≈ Rs.7509 (Ans.)
Hence, the amount of each installment is Rs.7509 .
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Now, if You want to Solve it with Direct formula Than :-
☛ installment in CI :- P(1 + R/100)^T = x[ {(1 + R/100)^(T-1)} + {(1 + R/100)^(T-2)} + {(1 + R/100)^(T-3)} + {(1 + R/100)^(T-4)} _____________ ]
where,
- P = Principal.
- R = Rate.
- T = Number of installments.
- x = Amount of installment.
Putting All our values Now, we get :-
☞ 13390[1 + 8/100]² = x[ (1 + 8/100)^(2 - 1) + (1 + 8/100)^(2-2)]
☞ 13390 * (27/25)² = x * [ 27/25 + 1 ]
☞ 13390 * (729/625) = x * (52/25)
☞ x = (13390 * 729 * 25) / (625 * 52)
☞ x = (1030 * 729) / (25 * 4)
☞ x = (750870) / 100
☞ x = Rs.7508.7 ≈ Rs.7509 (Ans.)
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Note :- in installment , we cant just find Amount , and Divide that by Our Time. That Process is wrong . As it is the amount paid After Each Year with interest . And after that , we have to give interest on Rest Amount. Read Question carefully and Think before solving.
Best of LUCK.
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Given : A sum of Rs. 13,390 was borrowed at 8% per annum compound interest and paid back in 2 years in two equal annual installments.
To Find : the amount of each installment (approximately)
Solution:
Amount of Loan = 13390
Let say Installment = P
R = 8 %
Interest for 1st Year = 13390 * 8 * 1 /100
= 1071 .2
Amount paid after 1 year = P Rs
Amount Remaining = 13390 + 1071.2 - P
= 14,461.2 - P
Interest in 2nd Year = (14,461.2 - P) * 8 * /100
Amount to be paid = 14,461.2 - P + (14,461.2 - P) * 8 * /100
= (14,461.2 - P)(1.08)
Amount Paid = P
(14,461.2 - P)(1.08) = P
=> P = 14,461.2 * 1.08 / 2.08
=> P = 7,508.7
Approx. 7509 Rs
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