Future Value of A Series Of Payments

Future Value  of A Series Of Payments : -

Calculate the Future value at the end of 5 years of the following series of payment at 10%   rate of interest.

R₁  = Rs.1000 at the end of 1^st year

R₂  = Rs.2000 at the end of 2^nd  year.

R₃  = Rs.3000 at the end of 3^rd  year.

R₄  = Rs.2000 at the end of 4^st year.

R₅ = Rs. 1500 at the end of 5^th year

V_n­  = R₁(1+i)^n-1 + R₂(1+i)^n-2 + R₃ (1+i)^n-3 + R₄ (1+i)^n-4 + R_n

      =  1000(1+.10)^5-1 + 2000(1+.10)^5-2 + 3000(1+.10)^5-3 + 2000(1+.10)^5-4 + 1500

      =  1000(1.10)⁴ + 2000(1.10)³ + 3000(1.10)² + 2000(1.10)¹  + 1500

      =   1000(1.464)+2000(1.3310)+3000(1.21)  +2000(1.10) +1500

      = 1464 + 2662 +3630 +2200+1500

V_n = 11456

Another Method : -

Using Compounding Factor Table

End of year	Amt of payment	No. of yrs compounded	Compounded Interest factor	Future value
1	1000	4	1.464	1464
2	2000	3	1.331	2662
3	3000	2	1.210	3630
4	2000	1	1.100	2200
5	1500	0	1	1500
				11456

Future value of  the end of 5 years = 11456