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A took loan from B the loan is to be repaired in annual installment of 2000 each the first installment is to be paid for 3 years from today and the last one is to be paid 8 years from today what is the value of loan today using a discount rate of 8%?
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A took loan from B the loan is to be repaired in annual installment of...
Calculation of Present Value of Loan

Given Information


  • Loan amount taken by A from B.

  • Loan repayment is in annual installments of 2000.

  • First installment is due after 3 years from today.

  • Last installment is due after 8 years from today.

  • Discount rate is 8%.



Calculation of Present Value of Loan

To calculate the present value of the loan, we need to find the present value of each installment and then add them up.


Calculation of Present Value of Each Installment

To calculate the present value of each installment, we will use the formula:

Present Value = Future Value / (1 + r)n

Where,


  • r = Discount rate = 8%

  • n = Number of years from today



Using the above formula, we get:


  • Present Value of First Installment = 2000 / (1 + 0.08)3 = 1571.55

  • Present Value of Second Installment = 2000 / (1 + 0.08)4 = 1453.60

  • Present Value of Third Installment = 2000 / (1 + 0.08)5 = 1345.88

  • Present Value of Fourth Installment = 2000 / (1 + 0.08)6 = 1250.09

  • Present Value of Fifth Installment = 2000 / (1 + 0.08)7 = 1163.37

  • Present Value of Sixth Installment = 2000 / (1 + 0.08)8 = 1084.67

  • Present Value of Seventh Installment = 2000 / (1 + 0.08)9 = 1012.85

  • Present Value of Eighth Installment = 2000 / (1 + 0.08)10 = 946.85



Calculation of Present Value of Loan

To calculate the present value of the loan, we will add up the present value of each installment:

Present Value of Loan = 1571.55 + 1453.60 + 1345.88 + 1250.09 + 1163.37 + 1084.67 + 1012.85 + 946.85 = 10728.96


Conclusion

The present value of the loan is 10728.96 using a discount rate of 8%.
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A took loan from B the loan is to be repaired in annual installment of 2000 each the first installment is to be paid for 3 years from today and the last one is to be paid 8 years from today what is the value of loan today using a discount rate of 8%?
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