Question

A person invests 8000 dollars in a bank. The bank pays 6.75% interest compounded quarterly. 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, we need to use the compound interest formula. For this specific scenario, the person must leave the money in the bank for 3.5 years.

Step-by-step explanation:

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

In this case, the principal amount is $8,000, the annual interest rate is 6.75%, and the interest is compounded quarterly. We need to solve for t.

10500 = 8000(1 + 0.0675/4)^(4t)

Dividing both sides by 8000 gives:

1.3125 = (1.016875)^(4t)

Taking the natural logarithm of both sides gives:

ln(1.3125) = 4t * ln(1.016875)

Dividing both sides by 4 * ln(1.016875) gives:

t = ln(1.3125) / (4 * ln(1.016875))

Using a calculator, we find that t is approximately 3.5. Therefore, the person must leave the money in the bank for 3.5 years to reach $10,500.