Question

A person invests 9500 dollars in a bank. The bank pays 5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 13200 dollars?

A = P(1 + r/n)ⁿᵗ

Answer 1

To calculate the time it takes for an investment to reach a certain value, you can use the formula for compound interest. In this case, the person must leave the money in the bank for approximately 4.4 years until it reaches $13,200.

Step-by-step explanation:

To calculate the time it takes for an investment to reach a certain value, you can use the formula for compound interest:

A = P(1 + r/n)ⁿᵗ

Where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, we have:

A = $13,200
P = $9,500
r = 0.05
n = 1 (compounded annually)

Substituting these values into the formula, we get:

$13,200 = $9,500(1 + 0.05/1)⁽ⁿᵗ⁾

Now we can solve for t:

(1.05)⁽ⁿᵗ⁾ = 13,200/9,500

(1.05)⁽ⁿᵗ⁾ = 1.3895

We can use logarithms to solve for t:

log((1.05)⁽ⁿᵗ⁾) = log(1.3895)

(ⁿᵗ⁾log(1.05) = log(1.3895)

ⁿᵗ⁾ = log(1.3895)/log(1.05)

ⁿᵗ⁾ ≈ 4.4 years

Therefore, the person must leave the money in the bank for approximately 4.4 years until it reaches $13,200.