You want to be able to withdraw the specified amount periodically from a payout annuity with...

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

regular withdraw: $1900
interest rate: 2%
frequency: quarterly
time: 28 years

Expert Solution

Payout annuities are typically used after retirement. With a payout annuity, you start with money in the account, and pull money out of the account on a regular basis. So basically we need to find out the starting amount that we need to keep in our account.

The formula for payout annuity is :

P₀ = 1900 * (1- ( 1 + (0.02/4))^{-28 * 4} ) / (0.02/4)

P₀ = 1900 * (1- (1.005)^{-28 * 4} ) / (0.005)

P₀ = 1900 * (1- 0.572) / (0.005)

P₀ = 1900 * 0.428 / (0.005)

P₀ = 813.2 / (0.005)

P₀ = $162,640

The account needs to hold $162,640 initially to make it possible.

Thankyou.

Colby Messinger answered 1 year ago

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