Question

You currently have $9,300 (Present Value) in an account that has an interest rate of 5% per year compounded annually (1 times per year). You want to withdraw all your money when it reaches $15,810 (Future Value). In how many years will you be able to withdraw all your money?

Answer 1

We can use the formula for the future value of a present sum of money:

FV = PV x (1 + r)^n

Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of compounding periods.

Substituting the given values, we have:

$15,810 = $9,300 x (1 + 0.05)^n

Dividing both sides by $9,300, we get:

1.7 = (1.05)^n

Taking the natural logarithm of both sides, we get:

ln(1.7) = ln(1.05)^n

Using the logarithmic property that ln(a^b) = b x ln(a), we can simplify the right side:

ln(1.7) = n x ln(1.05)

Dividing both sides by ln(1.05), we get:

n = ln(1.7) / ln(1.05)

Using a calculator, we get:

n ≈ 11.97

Therefore, it will take approximately 11.97 years (or about 12 years) to reach a future value of $15,810 and be able to withdraw all the money from the account.

Answer 2

This is a problem of time value of money, and we can use the formula for future value of a single sum to solve it. The formula is:

FV = PV x (1 + r)^n

where FV is the future value, PV is the present value, r is the interest rate per period, and n is the number of periods.

Plugging in the values given in the problem, we get:

$15,810 = $9,300 x (1 + 0.05)^n

Simplifying this equation, we get:

1.7 = (1.05)^n

Taking the natural logarithm of both sides, we get:

ln(1.7) = n x ln(1.05)

Solving for n, we get:

n = ln(1.7) / ln(1.05) ≈ 9.27 years

Therefore, it will take approximately 9.27 years to reach a future value of $15,810 and withdraw all the money.