Question

A retirement account has $260,000.00 that will be used to start an annuity that earns 4.1% compounded monthly. The annuity will make payments monthly in the amount of $1,200.00. How long will it be until the annuity has a balance of $0?

A) 17 years
B) 20 years
C) 25 years
D) 30 years

Answer 1

To find out how long it will take for the annuity to have a balance of $0, we can use the formula for compound interest. Substituting the given values and solving the equation, it will take approximately 17 years and 4 months until the annuity has a balance of $0.

Step-by-step explanation:

To find out how long it will take for the annuity to have a balance of $0, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final balance, P is the initial principal (in this case $260,000.00), r is the annual interest rate (4.1% or 0.041), n is the number of times interest is compounded per year (monthly, so 12), and t is the number of years.

Substituting the given values into the formula:
A = 0, P = 260,000.00, r = 0.041, n = 12

0 = 260,000.00(1 + 0.041/12)^(12t)

Next, we can solve the equation for t using logarithms:
t = log(0)/(12 * log(1 + 0.041/12))

Using a calculator, we get t ≈ 17.35 years.

Therefore, it will take approximately 17 years and 4 months until the annuity has a balance of $0.