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In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded annually?
- a)4 years
- b)3 years
- c)2 years
- d)1 year
Correct answer is option 'B'. Can you explain this answer?
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In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded ann...
⇒ n = 3 years
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In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded ann...
Problem:
In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded annually?
Solution:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case, we have:
P = Rs.1000
A = Rs.1331
r = 10% = 0.10
n = 1 (compounded annually)
We need to find t.
Step 1: Substitute the given values into the compound interest formula:
1331 = 1000(1 + 0.10/1)^(1*t)
Simplifying the equation:
1331 = 1000(1.10)^t
Step 2: Divide both sides of the equation by 1000:
1.331 = 1.10^t
Step 3: Take the logarithm of both sides of the equation to solve for t:
log(1.331) = log(1.10^t)
Using logarithm properties:
log(1.331) = t * log(1.10)
Step 4: Divide both sides of the equation by log(1.10):
t = log(1.331) / log(1.10)
Using a calculator, we can find the value of t:
t ≈ 3
Therefore, it will take approximately 3 years for Rs.1000 to amount to Rs.1331 at 10% p.a. compounded annually. Hence, the correct answer is option 'B'.
In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded annually?
Solution:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case, we have:
P = Rs.1000
A = Rs.1331
r = 10% = 0.10
n = 1 (compounded annually)
We need to find t.
Step 1: Substitute the given values into the compound interest formula:
1331 = 1000(1 + 0.10/1)^(1*t)
Simplifying the equation:
1331 = 1000(1.10)^t
Step 2: Divide both sides of the equation by 1000:
1.331 = 1.10^t
Step 3: Take the logarithm of both sides of the equation to solve for t:
log(1.331) = log(1.10^t)
Using logarithm properties:
log(1.331) = t * log(1.10)
Step 4: Divide both sides of the equation by log(1.10):
t = log(1.331) / log(1.10)
Using a calculator, we can find the value of t:
t ≈ 3
Therefore, it will take approximately 3 years for Rs.1000 to amount to Rs.1331 at 10% p.a. compounded annually. Hence, the correct answer is option 'B'.
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In what time will Rs.1000 amount to Rs.1331 at 10% p.a. compounded annually?a)4 yearsb)3 yearsc)2 yearsd)1 yearCorrect answer is option 'B'. Can you explain this answer?
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