24. Find the future value of annuity of Rs. 1,000 made annually for 7 years at interest rate of 14%
compounded annually. Given that (1.14)? = 2.5023
(a) 10,730.7
(b) 5,365.36
(C) 8,756
(d) 9,892.34
Answers
Given : annuity of Rs. 1,000 made annually for 7 years at interest rate of 14% compounded annually.
To Find : the future value
Solution:
Its not clear that value to be find at beginning of 7th year or at the end of 7 years.
Finding Both cased
annuity of Rs. 1,000 made annually for 7 years
calculating at end of 7 years
Value of Rs 1000 Deposited 1st year = 1000 ( 1 + 14/100)⁷
Value of Rs 1000 Deposited 2nd year = 1000 ( 1 + 14/100)⁶
Value of Rs 1000 Deposited 7th year = 1000 ( 1 + 14/100)¹
Total = 1000 ( 1 + 14/100)¹ + _____ 1000 ( 1 + 14/100)⁶ + 1000 ( 1 + 14/100)⁷
n = 7 r = 1.14
a = 1000 ( 1 + 14/100) = 1140
S = 1140 ( 1.14⁷ - 1)/(1.14 - 1)
=>S = 1140 ( 2.5023 - 1)/ 0.14 = 12,233 Rs
None of the given option matches
Calculating at beginning of 7 year
1000 + 1000 ( 1 + 14/100)¹ + _____ 1000 ( 1 + 14/100)⁶
a = 1000 r = r = 1.14 n = 7
=> S = 1000 ( 1.14⁷ - 1)/(1.14 - 1)
=>S = 1000( 2.5023 - 1)/ 0.14 = 10,730.7 Rs
10,730.7 Rs is the Future Value
option a matches for at beginning of 7 year
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