Question 1101888: You need Rs 100000 to buy a new television
If you have 6000 to invest at 5 percent compound anually how long you have to wait to buy the television
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the cost of the television is 100,000.
you have 6,000
the interest rate is 5% compounded annually.
the formula is f = p * (1+r) ^ n
f is the future value
p is the present value
r is the interest rate per tiem period
n is the number of time periods.
in your problem:
f = 100,000
p = 6,000
r = .05
n = what you want to find.
the formula becomes 100,000 = 6,000 * 1.05 ^ n
divide both sides of this formula by 6,000 to get 100,000 / 6,000 = 1.05 ^ n
simplify to get 100/6 = 1.05 ^ n
take the log of both sides of this equation to get:
log(100/6) = log(1.05 ^ n)
since log(1.05 ^ n) is equal to n * log(1.05), the equation becomes:
log(100/6) = n * log(1.05)
divide both sides of this equation by log(1.05) to get:
log(100/6) / log(1.05) = n
solve for n to get:
n = 57.66348125.
it would take 57.66348125 years for 6,000 rs to becomes 100,000 rs if you invest it at 5% per year compounded annually.
6,000 * 1.05 ^ (57.66348125) is equal to 100,000.
that's a life time.
perhaps you meant the cost of the television is 10,000 rs?
if that's the case, then the formula becomes:
10,000 = 6,000 * 1.05 ^ n
divide both sides by 6,000 and simplify to get 10/6 = 1.05 ^ n
take the log of both sides and simplify to get log(10/6) = n * log(1.05)
divide both sides by log(1.05) to get log(10/6) / log(1.05) = n
solve for n to get n = 10.46984843.
6,000 * 1.05 ^ 10.46984843 = 10,000.
if the cost of the television was 10,000 rs, it would take you 10.46984843 years for your invested amount of 6,000 rs to become equal to that.
you would still have to wait a very long time, but 10 years is certainly better than 57.
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