To solve this problem, we will 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, so 5% becomes 0.05).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

We want to find out when the initial amount of money will triple, so we can set A = 3P. Then we can solve for t.

3P = P(1 + 0.05/365)^(365t)

Divide both sides by P to get:

3 = (1 + 0.05/365)^(365t)

Take the natural logarithm (ln) of both sides to get:

ln(3) = 365t * ln(1 + 0.05/365)

Solve for t:

t = ln(3) / (365 * ln(1 + 0.05/365))

Using a calculator, we find that t ≈ 22.4 years. So, it will take approximately 22.4 years to triple your money with a 5% annual interest rate compounded daily.

Question

To solve this problem, we will 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, so 5% becomes 0.05).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

We want to find out when the initial amount of money will triple, so we can set A = 3P. Then we can solve for t.

3P = P(1 + 0.05/365)^(365t)

Divide both sides by P to get:

3 = (1 + 0.05/365)^(365t)

Take the natural logarithm (ln) of both sides to get:

ln(3) = 365t * ln(1 + 0.05/365)

Solve for t:

t = ln(3) / (365 * ln(1 + 0.05/365))

Using a calculator, we find that t ≈ 22.4 years. So, it will take approximately 22.4 years to triple your money with a 5% annual interest rate compounded daily.

Knowee AI · Accepted Answer

To solve this problem, we will 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, so 5% becomes 0.05).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

We want to find out when the initial amount of money will triple, so we can set A = 3P. Then we can solve for t.

3P = P(1 + 0.05/365)^(365t)

Divide both sides by P to get:

3 = (1 + 0.05/365)^(365t)

Take the natural logarithm (ln) of both sides to get:

ln(3) = 365t * ln(1 + 0.05/365)

Solve for t:

t = ln(3) / (365 * ln(1 + 0.05/365))

Using a calculator, we find that t ≈ 22.4 years. So, it will take approximately 22.4 years to triple your money with a 5% annual interest rate compounded daily.

How long (in years) will it take to triple your money if it is invested in a certificate of deposit (CD) that pays 5% annual interest compounded daily? Round to the nearest tenth of a year. (Use 365 days for each year.)

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