Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the end of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded semi-annually.

Question

Quizplus · Accepted Answer

We need to use the formula for the future value of an annuity due:

FV = PMT((1 + r/n)^(nt) - 1)(n/r)

where:

PMT = $4,420 (monthly payment)
r = 4.9% (annual rate)
n = 2 (semi-annual compounding)
t = 40 (20 years x 12 months)

First, we need to find the future value needed to receive $10,000 per month for 20 years. This is:

FV_needed = $10,000((1 + 0.049/12)^(12*20) - 1)/(0.049/12) = $2,047,404.31

Now, we can find the time it will take to reach this amount with a monthly payment of $4,420 and a semi-annual rate of 2.45% (since the compounding is semi-annual):

$2,047,404.31 = $4,420((1 + 0.0245)^(2t) - 1)/(0.0245)

Solving for t, we get:

t ≈ 18.11 years

Therefore, Siri should retire in 18.11 years from today.

Siri Plans to Retire When Her Simple Annuity Savings Account