A debt is Rs 5000/ due 5 years hence and another sum of Rs 7500/ due 8 years
hence are to be paid off by a single payment 6 years hence. If rate of interest
8% per anrum effectively, how much is this payment?
How an equation of money is the sum of the values on a given date of one set of
obligations is the same as the sum of the values, on the same date of another set
of obligations. Justify your explanation with the help of an exam
Answers
Answer:
Example 5 : Mr. X owes Rs. 1,000 due in 1 year and Rs. 3,000 due in 4 years. He agrees
to pay Rs. 2,000 today and the reminder in 2 years. How much he pay at the end of 2 years if
the money is worth 5% compounded semi-annually ?
Solution: Let Rs. x be the final payment due at the end of 2 years.
The focal date is 2 years.
r = 5% = 0.05
Interest is calculated half-yearly
. . i = 0~5 = 0.025
The old obligations and the new obligations are shown in the following table.
Old Obligations Value of each at New Obligations Value of each at
focal date focal date
Rs. 1,000 due in 1 year 1,000 (1.025)1" 2 Rs. 2,000 today 2,000 (1.025)2" 2
Rs. 3,000 due in 4 years 1,000 (1.025)- 2" 2 Rs. x due in 2 years. x
The equation of value is given by :
Sum of the values of old Obligations} _ {sum of the values of new obligations
at focal date - at focal date
The required equation
. . 1,000 (1.025)2 + 3,000 (1.025)-4 = 2,000 (1.025)4 + x
1,050.625 + 2,717.852 = 2,207.626 +x
3,768.477 = 2,207.626 + x
x = Rs. 1,560.85
. . The amount to be paid is Rs. 1,560.85.
Example 6 : A debt of Rs. 2,000 due in 2 years and Rs. 3,000 due in 7 years is to be
repaid by a single payment of Rs. 1,000 now and 2 equal payments which are due 1 year from
now and 4 years from now. If the interest rate is 6% compounded annually, how much will be
the equal payments ?
I
Solution: Let Rs. x be the equal payment.
The focal date is 4 years
i = r = 6% = 0.06
The old obligations and now obligations are shown in the following table:
Old Obligations Value of each at New Obligations Value of each at
focal date focal date
._---
Rs. 2,000 due in 2 years 2,000 (1.06)2 Rs. 1,000 now 1,000 (1.06)4
Rs. 3,000 due in 7 years 3,000 (1.06)-3 Rs. x in 1 year x (1.06)3
Rs. x due in 4 years x