MAT$143$ Lab $3$

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Part $1$:

According to Northwestern Mutual, $56\%$ of adults in the US don't know how much money they will need to save to retire. This can be problematic when settingup your long$-$term financial goals. In this activity, you will explore a financial instrument, called a payout annuity, that can be used to invest after retirement and maintain a steady income.

Suppose you want to have an after$-$retirement annual income of $$50,000$ for $20$ years.

Suppose you plan to place your retirement fund into an account that does not earn interest. How much money would you need in the account by the time you retire?

$50,00020=1,000,000in$ atotal $of$

a $20$ year period

$=$$$1,000,000$ in account by the time of petirement

Without further investing, your retirement fund will sit idle when it could be earning interest. A payout annuity provides regular withdrawals while allowing your balance to earn interest. The following formula is used to calculate the value of a payout annuity that compounds annually and has annual withdrawals.

$P=\frac{d(1-(1+r{)}^{-N})}{r}$