Question

$500 were deposited into an account with

a 5% interest rate, compounded monthly.
How many years was it in the bank if the
current amount is $2469?
t = [?] years
Round to the nearest year.

Answer 1

Answer: 15 years

Explanation:

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

Where:

A = the final amount

P = the principal (initial deposit)

r = the interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

In this case, we have:

A = $2469

P = $500

r = 5% = 0.05

n = 12 (compounded monthly)

Substituting these values into the formula, we have:

$2469 = $500(1 + 0.05/12)^(12t)

Dividing both sides of the equation by $500, we get:

4.938 = (1.00417)^(12t)

To solve for t, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):

ln(4.938) = ln[(1.00417)^(12t)]

Using the property of logarithms, we can bring down the exponent:

ln(4.938) = 12t * ln(1.00417)

Now, we can solve for t by dividing both sides by 12 times ln(1.00417):

t = ln(4.938) / (12 * ln(1.00417))

Using a calculator, we find:

t ≈ 14.58

Rounding to the nearest year, the money was in the bank for approximately 15 years.