Question

You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.

Answer 1

The question is incomplete. The complete question is :

You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.

Regular withdrawal    $ 2200

Interest rate                        2%

Frequency                   Monthly

Time                                20 years

Solution :

Given :

Monthly withdrawal = $ 2200

Interest rate = 2%

Frequency = monthly

Time = 20 years

        = 20 x 12 = 240 months

Formula used :

$w=\frac{[PZ^{r-1}(Z-1)]}{[Z^Y-1]}$         with Z = 1 + r

where, w = monthly withdrawal

P = principal amount

r = monthly interest rate

Y = Number of months

So, w = 2200

     r = 2% = 0.02

     Z = 1 + r

        = 1 + 0.02 = 1.02

Y = 240

Therefore,

$2200=\frac{P(1.02)^{240-1}(1.02-1)}{(1.02)^{240-1}(1.02-1)}$

$P=\frac{2200(115.888-1)}{113.6164(0.02)}$

   = 111,231829

   ≈ 111,232 (rounding off)

Thus, the account balance = $ 111,232