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Madhu had availed a loan of Rs. 120000 @ 12%, which she has to pay in 6 equal annual installments. Calculate the amount of installment?
a. 21897
b. 27897
c. 28197
d. 29187
Ans - d
Solution:
P = 120000
R = 12% p.a.
(SINCE PAYMENT IS TO ANNUALY, NOT Monthly, Rate IS NOT divided by 12)
T = 6 yrs
(SINCE PAYMENT IS TO BE ANNUALY, NOT Monthly, Time IS NOT multiplied with 12)
So, we can well use EMI formula in this question as we did in questions no 4, 5, 6 & 7
The formula of EMI = P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
EMI = 120000 × 0.12 × 1.12^6 ÷ (1.12^6 – 1)
= (120000*0.012*1.9738) ÷ 0.9738
= 28423 / 0.9738
= 29187
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Rajesh borrowed Rs. 50000 from the bank @ 12% p.a. for 1 year, payable on EMI basis. The amount of EMI will be?
a. 4424.24
b. 4244.24
c. 4424.44
d. 4442.44
Ans - d
Solution:
P = 50000
R = 12% / 12 = 0.01% (In EMI or Equated Monthly Instalment, we need to find monthly rate, so we divide rate by 12)
T = 1*12 = 12 (In EMI or Equated Monthly Instalment, we multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 50000*0.01*(1+0.01)^12 ÷ {(1+0.01)^12 – 1}
= (50000*0.01*1.126825) ÷ 0.126825
= 563.4125 / 0.126825
= 4442.44
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X borrowed Rs. 100000 from the bank @ 24% p.a. for 1 year, payable on EMI basis. The amount of EMI will be?
a. 6594
b. 6954
c. 9456
d. 9546
Ans - c
Solution:
P = 100000
R = 24% / 12 = 2% (In EMI or Equated Monthly Instalment, we need to find monthly rate, so we divide rate by 12)
T = 1*12 = 12 (In EMI or Equated Monthly Instalment, we multiply time with 12)
The formula of EMI = P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
So,
EMI = 100000*0.02*(1+0.02)^12 ÷ {(1+0.02)^12 – 1}
= (100000*0.02*1.268242) ÷ 0.268242
= 2536.484 / 0.268242
= 9456
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A person borrowed an amount of Rs. 50000 for 8 years @ 18% ROI. What shall be monthly payment?
a. 916.86
b. 961.86
c. 986.16
d. 996.16
Ans - c
Solution:
P = 50000
R = 18 % ÷ 12 = 0.015% (In EMI, divide rate by 12)
T = 8 *12 = 96 (In EMI, multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 50000 * 0.015 * 1.015^96 ÷ (1.015^96 – 1)
= 986.16 Ans
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A person borrowed Rs. 10000 from the bank @ 12% p.a. for 1 year, payable on EMI basis. What is the amount of EMI?
a. 848.48
b. 884.48
c. 888.48
d. 844.88
Ans - c
Solution:
P = 10000
R = 12% / 12 = 0.01% (In EMI or Equated Monthly Instalment), we need to find monthly rate, so we divide rate by 12)
T = 1 *12 = 12 (In EMI or Equated Monthly Instalment, we multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 10000*0.01*(1+0.01)^12 ÷ {(1+0.01)^12 – 1}
= 888.48 Ans
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A person raised a house loan of Rs. 10 lac @ 12% ROI repayable in 10 years. Calculate EMI.
a. 13447
b. 13474
c. 14347
d. 14374
Ans - c
Solution:
P = 10 lac
R = 12% / 12 = 0.01% (In EMI or Equated Monthly Instalment), we need to find monthly rate, so we divide rate by 12)
T = 10 *12 = 120 (In EMI or Equated Monthly Instalment, we multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 1000000*0.01*(1+0.01)^120 ÷ {(1+0.01)^120 – 1}
= 14347 Ans
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You will be receiving Rs. 100000 at the end of each year for the next 15 years. If the current discount rate for such a stream of cash is 9%, find the present value of cash flow.
a. 800669
b. 806069
c. 860609
d. 866009
Ans - b
Solution:
Since 100000 is like EMI. So, to find P, we use the formula of EMI
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
100000 = P × 0.09 × 1.09^15 ÷ (1.09^15 – 1)
100000 = P × 0.09 x 3.64248 ÷ 2.64248
264248 = P x 0.32782
P = 806069
This can be done with PV (OA) Present Value Ordinary Annuity too.
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A person wants to borrow Rs. 25000 immediately and another Rs. 20000 after a period of 2 years @ 10% interest. He wants to pay it in monthly installments for 5 years. Calculate the amount of monthly payment?
a. 879.29
b. 897.29
c. 789.29
d. 798.29
Ans - a
Hint:
Present Value of 20000 for 2 years @ 10% = 20000 ÷ 1.0083324 = 16388.07
So, total amount today= 25000 + 16388.07 = 41388.07
T = 5 × 12 = 60 months and R = 10% p.a. = 10/1200 = 0.00833
Now, apply EMI formula.
Ans is 879.29
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Anita borrowed an amount of Rs. 500000 for 10 years @ 9% ROI. What shall be monthly payment?
a. 8445
b. 8454
c. 8545
d. 8554
Ans - a
Solution:
P = 500000
R = 9 % ÷ 12 = 0.0075% (In EMI, divide rate by 12)
T = 10*12 = 120 (In EMI, multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 500000 * 0.0075 * 1.0075^120 ÷ (1.0075^120 – 1)
= (500000*0.0075*2.4514) ÷ 1.4514
= 12257 / 1.4514
= 8445
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Ram availed a house loan of Rs. 20 lac @ 12% ROI repayable in 15 years. Calculate EMI.
a. 23004
b. 23404
c. 24003
d. 24303
Ans - c
Solution:
P = 10 lac
R = 12% / 12 = 0.01% (In EMI or Equated Monthly Instalment), we need to find monthly rate, so we divide rate by 12)
T = 12*15 = 180 (In EMI or Equated Monthly Instalment, we multiply time with 12)
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 2000000*0.01*(1+0.01)^180 ÷ {(1+0.01)^180 – 1}
= (2000000*0.01*5.9958) ÷ 4.9958
= 119916 / 4.9958
= 24003
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Anvita wants to receive a fixed amount for 10 years by investing Rs. 10 lacs @ 12% ROI. How much he will receive annually?
a. 167894
b. 176984
c. 187964
d. 196874
Ans - b
Solution:
P = 10 lac
R = 12% p.a.
(SINCE PAYMENT IS TO BE RECEIVED ANNUALY, NOT Monthly, Rate IS NOT divided by 12)
T = 10 yrs
(SINCE PAYMENT IS TO BE RECEIVED ANNUALY, NOT Monthly, Time IS NOT multiplied with 12)
So, we can well use simple EMI formula in this question.
The formula of EMI =
--------------------------------------------------
P * R * (1 + R)^T ÷ { (1 + R)^T - 1 }
--------------------------------------------------
So,
EMI = 1000000 * 0.12 * 1.12^10 ÷ (1.12^10 – 1)
= (1000000*0.012*3.1058) ÷ 2.1058
= 372702 / 2.1058
= 176984
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