financial spreadsheet, so we will limit our discussion here to the first two types of annuities. annuity period. The equation is:

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

Each payment of an annuity due is compounded for one

$(0$ period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one $-$ Selectperiod. The equation is:

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

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

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

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 $4$ years? Do not round intermediate calculations. Round your answer to the ne $\frac{?}{\text{b}\text{a}\text{r}}(f)$ rest cent. $

b$.$ Assume that your deposits will begin today. What amount will be in your account after $4$ years? Do not round intermediate calculations. Round your answer to the nearest cent. $ be made one year after you retire and you anticipate that your retirement account will earn $15\%$ annually.

a$.$ What amount do you need in your retirement account the day you retire? Do not round intermediate calculations. Round your answer to the nearest cent. $