The time in which a sum of money will be double at 5% p.a C.I isa.10 yearsb.12 yearsc.14.2 yearsd.15.2 years

To solve this problem, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, we want to find out the time (t) it takes for an initial sum (P) to double (A = 2P) with an annual interest rate of 5% (r = 0.05) compounded annually (n = 1).

So, we have:

2P = P(1 + 0.05/1)^(1*t)

Solving for t, we get:

2 = (1 + 0.05)^t

Taking the natural logarithm (ln) of both sides, we get:

ln(2) = t * ln(1.05)

Finally, solving for t, we get:

t = ln(2) / ln(1.05)

Using a calculator, we find that t ≈ 14.2 years.

So, the correct answer is c. 14.2 years.

To solve this problem, we can use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, we want to find out the time (t) it takes for the initial amount (P) to double. This means that A is 2P. The interest rate (r) is 5% or 0.05 in decimal form, and we'll assume that interest is compounded once a year, so n is 1.

So, we have:

2P = P(1 + 0.05/1)^(1*t)

We can simplify this to:

2 = (1 + 0.05)^t

Now, we need to solve for t. This is a bit tricky, but we can use the natural logarithm (ln) to help us:

ln(2) = t * ln(1 + 0.05)

t = ln(2) / ln(1 + 0.05)

If you calculate this, you'll find that t is approximately 14.2 years. So, the answer is c. 14.2 years.

To solve this problem, we can use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, we want to find out the time (t) it takes for an initial sum (P) to double (A = 2P) with an annual interest rate of 5% compounded annually (r = 0.05, n = 1).

So, we have:

2P = P(1 + 0.05/1)^(1*t)

Solving for t, we get:

2 = (1 + 0.05)^t

Taking the natural logarithm (ln) of both sides, we get:

ln(2) = t * ln(1.05)

Finally, solving for t, we get:

t = ln(2) / ln(1.05)

If you calculate this, you will find that t is approximately 14.2 years. So, the correct answer is c. 14.2 years.