Question

Q no 6
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 is
8% per annum effectively, how much is this payment?
on
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 the same date of another set
of obligations. Justify your explanation with the help of an example.​

Answer 1

Given :-

• A debt is Rs 5000/ due 5 years hence.
• Another sum of Rs 7500/ due 8 years hence.
• A single payment 6 years hence .
• Rate of interest = 8% per annum effectively .

Concept and formula used :-

• we used Simple interest, only if it is mentioned in the problem, otherwise it is treated as compound interest.

• Value of debt after due date at given rate per period is taken as +ve.

• Value of debt before due date at at given rate per period is taken as -ve.

• Sum of the values of old ebligations is equal to sum of the values of new obligations.

Solution :-

Let us assume that, Rs.x is the Amount due in 6 years.

Than,

old obligation :-

→ 5000 due in 5 years = P(1 + r/100)^T

→ 5000(1 + 8/100)^(6-5)

→ 5000(1 + 2/25)

→ 5000 * (27/25)

→ Rs.5400 .

Another old obligation :-

→ 7500 due in 8 years = P(1 + r/100)^T

→ 7500(1 + 8/100)^(6 - 8)

→ 7500(1 + 2/25)^(-2)

→ 7500 * (27/25)^(-2)

→ 7500 * (25/27)²

→ 7500 * (625/729)

→ Rs.6430.04 .

And,

→ New obligation = Rs. x at the end of 6 years.

Now, we know that,

→ Sum of the values of old ebligations = sum of the values of new obligation.

Therefore,

→ 5400 + 6430.04 = x

→ x = Rs.11830.04 (Ans.)

∴ The Required payment is Rs.11830.04.

Answer 2

Given :  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 .  rate of interest is  8% per annum effectively

To find :  how much is this payment?

Solution:

R = 8 %

Let say Present debt is x  for   debt   Rs 5000/ due 5 years hence

Hence 5000 = x( 1 + 8/100)⁵

=> 5000 = x ( 1.08)⁵

=>  x = 5000 (1.08)⁻⁵

Let say Present debt is y  for   debt   Rs 7500/ due 8 years hence

Hence 7500 = y( 1 + 8/100)⁸

=> y = 7500 ( 1.08)⁻⁸

Total debt  at present =  5000 (1.08)⁻⁵ + 7500 ( 1.08)⁻⁸

To be paid 6 years Hence  = A

A = ( 5000 (1.08)⁻⁵ + 7500 ( 1.08)⁻⁸ ) ( 1  + 8/100)⁶

=> A = ( 5000 (1.08)⁻⁵ + 7500 ( 1.08)⁻⁸ ) ( 1.08)⁶

=> A = 5000 (1.08) +  7500 ( 1.08)⁻²

=> A = 5400 + 6,430

=> A = 11,830

Payment = Rs 11830

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