Time Value of Money: Annuities

$FV{A}_N=PMT[\frac{(1+I{)}^N}{\text{I}}-\frac{1}{\text{I}}]$

$FV{A}_{\text{d}\text{u}\text{e}}=FV{A}_{\text{o}\text{r}\text{d}\text{i}\text{n}\text{a}\text{r}\text{y}}(1+I)$

The present value of an ordinary annuity, PVA $,$ is the value today that would be equivalent to the annuity payments $($PMT$)$ received at fixed intervals over the annuity period. The equation is:

$PV{A}_N=PMT[\frac{1}{\text{I}}-\frac{1}{I(1+I{)}^N}]$

$PV{A}_{\text{d}\text{u}\text{e}}=PV{A}_{\text{o}\text{r}\text{d}\text{i}\text{n}\text{a}\text{r}\text{y}}(1+I)$

One can solve for payments $($PMT$),$ periods $($N$),$ and interest rates $($I$)$ for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet.

a$.$ What amount will be in your account at the end of $5$ years?

$

b$.$ Assume that your deposits will begin today. What amount will be in your account after $5$ years?

$

answers to the nearest cent.

a$.$ What amount do you need in your retirement account the day you retire?

b$.$ Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire?