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Question 428540: You make a deposit of 2000 € into your account. The interest rate is 5% and the interest is added into the account first after one year and then annually. How long will it take your savings to grow to 10000 €?
Found 2 solutions by Gogonati, mananth:
Answer by Gogonati(855)   (Show Source):
You can put this solution on YOUR website! Solution:Since the interest is added annually we know that,  ,
where A(t) is the amount of investment after t years, P is the initial investment and r is the interest rate. Substitute the given values and we have:
 , Divide both sides by 2000,
 , Take ln of both sides,
ln(5)=tln(1.05), Divide both sides by ln(1.05),
t=ln(5)/ln(1.05)
t=33
Answer: Approximately after 33 years our investment will be 10,000 Eu.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Principal P = 2000
Amount= 10000
years=n
compounded 1
Amount = P*((n+r)/n)^n
10000 = 2000 *( 1 + 0.05 )^ n
5 = *( 1 + 0.05 )^ n
ln 5 = n ln 1.05
1.61 = n 0.05
32.99 = n
Say 33 years
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