Question

A person invests 5000 dollars in a bank. The bank pays 5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 10500 dollars?

Answer 1

To find out how long the person must leave the money in the bank until it reaches $10,500, use the compound interest formula.

Step-by-step explanation:

To find out how long the person must leave the money in the bank until it reaches $10,500, we can use the compound interest formula. The formula is given by: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.

1. First, let's convert the interest rate to a decimal. 5% becomes 0.05.
2. We know that P = $5,000 and A = $10,500. Plug in these values along with the values for r and n into the compound interest formula.
3. Now, we need to solve for t. Divide both sides of the equation by P and isolate t on one side.
4. Finally, use logarithms to solve for t. Take the logarithm of both sides of the equation, and use the logarithm identities to simplify and solve for t.

The value of t represents the time, in years, that the person needs to leave the money in the bank until it reaches $10,500. Round the answer to the nearest tenth of a year.

Answer 2

To find the time, we use the formula for compound interest. Substituting the values and solving for t, we find that the person must leave the money in the bank for approximately 8.8 years until it reaches $10500.

Step-by-step explanation:

To find the amount of time the person must leave the money in the bank, we can use the formula for compound interest:

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

Where:

1. A is the future value of the investment
2. P is the principal amount (initial investment)
3. r is the annual interest rate (in decimal form)
4. n is the number of times interest is compounded per year
5. t is the number of year

In this problem, the principal (P) is $5000, the interest rate (r) is 5% (or 0.05), and the future value (A) is $10500. Since the interest is compounded monthly, the number of times compounded per year (n) is 12.

Substituting the given values into the formula:

$10500 = $5000(1 + 0.05/12)^(12t)

Solving for t using a logarithm or a calculator:

t ≈ 8.8 years (to the nearest tenth of a year)

Therefore, the person must leave the money in the bank for approximately 8.8 years until it reaches $10500.