Question

In return of a promise to pay Rs. 500 at the end of 10 years, a person agrees to pay Rs. 100 now, Rs 200 at the end of 6 years and a final payment at the end of 12 years. If the rate of interest is 2% per annum effective, what should be the final payment?​

Answer 1

Answer:

Rs 168.14

Step-by-step explanation:

Let X be the final payment due at the end of 12 years. Using 12 years and hence from today as the focal date. The old and new the old and new obligations are as under

Old obligations= Rs 500 due at the end of 10 years

Value of each old obligation at focal date= $500(1.02)^{2}$

New obligations= Rs 100 now, Rs 200 at the end of six years, Rs X at the end of 12 years

Value of each new obligations at focal date = $100(1.02)^{12}$, $200(1.02)^{6}$and  X

The equation of value at focal date is,

$500(1.02)^{2}$=$100(1.02)^{12}$+$200(1.02)^{6}$+X

X= $500(1.02)^{2}$- $100(1.02)^{12}$- $200(1.02)^{6}$

X= 500(1.0404)- 100(1.268242)- 200(1.126162)

X= 520.20- 126.8242- 225.2324

X= 168.14