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 1st year
R2 = Rs.2000 at the end of 2nd year.
R3 = Rs.3000 at the end of 3rd year.
R4 = Rs.2000 at the end of 4st year.
R5
= Rs. 1500 at the end of 5th year
Vn
= R1(1+i)n-1
+ R2(1+i)n-2 + R3 (1+i)n-3 + R4
(1+i)n-4 + Rn
=
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
Vn
= 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
