How much needs to be initially deposited into an account earning $3\mathrm{.}25\%$ interest compounded semi $-$ annually in order to have $ at the end of $6$ years $?$

Consumer Mathematics

percent $of$ change $=\frac{\text{n}\text{e}\text{w}\text{a}\text{m}\text{o}\text{u}\text{n}\text{t}-\text{b}\text{a}\text{s}\text{e}\text{a}\text{m}\text{o}\text{u}\text{n}\text{t}}{\text{b}\text{a}\text{s}\text{e}\text{a}\text{m}\text{o}\text{u}\text{n}\text{t}}$

$($# $19)$ Simple Interest $I=Prt$

$($# $20)$ Future Value of a Simple Interest Account:

$A=P+I=P(1+rt)$

$($# $21)$ Future Value of Compound Interest Account $($compounded periodically$)$: $A=P(1+\frac{r}{m}{)}^n$

where $m=$ the number of compounding cycles per year, $n=$ the total number of compounding cycles

$($# $22)$ Future Value of a Continuous Compound Interest: $A=P{e}^{rt}$

Annuities that Grow $($account balance increases over time$)$

$\backslash$table$[[($# $23),R=\frac{A(\frac{r}{m})}{(1+\frac{r}{m}{)}^n-1},\backslash$table$[[$A is the future value of the account$],[$R is the fixed periodic transaction $($deposit$)],[r$ is the interest rate as a decimal$],[m$ is number of compound periods in a year$],[n$ is the total number of regular transactions$]]]]$

Annuities that Decay $($account balance decreases over time$)$

$\backslash$table$[[($# $25)$ Amortization of a loan:,$\backslash$table$[[P=$ the present value of the account$],[R=$ regular periodic payment to amortize the loan $($or$],[$the amount of the regular periodic withdraw$)],[r$ is the interest rate as a decimal$],[m$ is number of compound periods in a year$],[n$ is the total number of regular transactions$]]],[($# $26)$ Present Value of an Annuity:,$],[P=\frac{R*[(1+\frac{r}{m}{)}^n{)}^n-1}{(\frac{r}{m})(1+\frac{r}{m}{)}^n},]]$