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A finance company declares that, with Compound Interest, a sum of money deposited by anyone will become 8 times in 3 yrs. If the same amount is deposited at the same compound rate of interest, then in how many yrs it will become 16 times?
- a)4 yrs
- b)5 yrs
- c)6 yrs
- d)7 yrs
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A finance company declares that, with Compound Interest, a sum of mone...
23 (8 times) → 3 years
24 (16 times) → ?
Total Number of years = 3 x 4/3 = 4 years
24 (16 times) → ?
Total Number of years = 3 x 4/3 = 4 years
Most Upvoted Answer
A finance company declares that, with Compound Interest, a sum of mone...
Given:
- A sum of money deposited with compound interest becomes 8 times in 3 years.
- The same amount is deposited at the same compound rate of interest.
- We need to find the number of years it will take for the amount to become 16 times.
Formula for Compound Interest:
The formula for compound interest is given by:
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 = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
Calculating the Compound Interest:
Let's assume the principal amount deposited is P.
After 3 years, the amount becomes 8 times, so we have:
8P = P(1 + r/n)^(3n)
Simplifying the equation:
8 = (1 + r/n)^(3n)
Taking the cube root on both sides:
2 = 1 + r/n
Simplifying further:
r/n = 1
Therefore, the rate of interest is equal to the number of times it is compounded per year.
Calculating the Time for Amount to Become 16 times:
Now, let's find the time it will take for the amount to become 16 times.
We know that:
16P = P(1 + r/n)^(tn)
Simplifying the equation:
16 = (1 + r/n)^(tn)
Since we found earlier that r/n = 1, the equation becomes:
16 = (1 + 1)^t
Simplifying further:
16 = 2^t
Taking the logarithm on both sides:
log(16) = log(2^t)
Using the logarithmic property:
log(16) = t * log(2)
Simplifying:
t = log(16) / log(2)
Calculating the value:
t = 4
Therefore, it will take 4 years for the amount to become 16 times.
Hence, the correct answer is option A) 4 years.
- A sum of money deposited with compound interest becomes 8 times in 3 years.
- The same amount is deposited at the same compound rate of interest.
- We need to find the number of years it will take for the amount to become 16 times.
Formula for Compound Interest:
The formula for compound interest is given by:
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 = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
Calculating the Compound Interest:
Let's assume the principal amount deposited is P.
After 3 years, the amount becomes 8 times, so we have:
8P = P(1 + r/n)^(3n)
Simplifying the equation:
8 = (1 + r/n)^(3n)
Taking the cube root on both sides:
2 = 1 + r/n
Simplifying further:
r/n = 1
Therefore, the rate of interest is equal to the number of times it is compounded per year.
Calculating the Time for Amount to Become 16 times:
Now, let's find the time it will take for the amount to become 16 times.
We know that:
16P = P(1 + r/n)^(tn)
Simplifying the equation:
16 = (1 + r/n)^(tn)
Since we found earlier that r/n = 1, the equation becomes:
16 = (1 + 1)^t
Simplifying further:
16 = 2^t
Taking the logarithm on both sides:
log(16) = log(2^t)
Using the logarithmic property:
log(16) = t * log(2)
Simplifying:
t = log(16) / log(2)
Calculating the value:
t = 4
Therefore, it will take 4 years for the amount to become 16 times.
Hence, the correct answer is option A) 4 years.
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A finance company declares that, with Compound Interest, a sum of money deposited by anyone will become 8 times in 3 yrs. If the same amount is deposited at the same compound rate of interest, then in how many yrs it will become 16 times?a)4 yrsb)5 yrsc)6 yrsd)7 yrsCorrect answer is option 'A'. Can you explain this answer?
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