an amount gets doubled in 15 years with compund intrest.In how many years amount will become 8 times,using the same compund intrest ?

an amount gets doubled in 15 years with compund intrest.In how many years amount will become 8 times,using the same compund intrest ?

S = P(1 + i)^n where P = the invested amount, i = the decimal periodic interest rate and n = the number of inrterest paying periods.

Therefore, 2 = 1(1 + i)15 (assuming interest compounded yearly)

Solving, i = .04729 making the annual interest rate of 4.729%.

At the same interest rate and AS/P = 8,
8 = (1.047829)^n.

solving, n = ~45 years.

Checking, S = 1(1.04729)^45 = ~8.

To determine the number of years it takes for an amount to become 8 times its original value with compound interest, you can use the concept of the compound interest formula.

The formula for compound interest is given by:
A = P(1 + r/n)^(nt)

Where:
A is the final amount
P is the principal (initial amount)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years

In this case, we know that the amount becomes doubled (2 times) in 15 years. So, we can set up the equation:

2P = P(1 + r/n)^(n*15)

Simplifying the equation, we get:

2 = (1 + r/n)^(15n)

Now, we need to find the number of years it takes for the amount to become 8 times its original value. So, we want to solve for t in the equation:

8P = P(1 + r/n)^(nt)

Simplifying the equation, we get:

8 = (1 + r/n)^(nt)

To find the number of years, we can divide the second equation by the first equation:

(1 + r/n)^(nt) / (1 + r/n)^(15n) = 8 / 2

Simplifying further:

(1 + r/n)^(nt - 15n) = 4

Now, we need to solve for t in this equation. Since the base and the exponent are the same, we can equate the exponents:

nt - 15n = 2

Simplifying the equation, we get:

t - 15 = 2/n

Rearranging the equation, we find:

t = 15 + 2/n

Therefore, the amount will become 8 times its original value after t years, where t is given by:

t = 15 + 2/n

Please note that to calculate the exact value of t, you will need to know the specific interest rate (r) and the compounding frequency (n).