Answer:
$285,413.23
Step-by-step explanation:
We know the annuity formula is given by,
[tex]P=\frac{r \times PV}{1-(1+r)^{-n}}[/tex],
where P = regular payment, PV = present value, r = rate of interest and n = time period.
According to the question, we need to find the money to be deposited at the start of the year i.e. PV
So, re-arranging the formula and substituting the values gives us,
[tex]PV=\frac{25312 \times [1-(1+0.062)^{-20}]}{0.062}[/tex]
i.e. [tex]PV=\frac{25312 \times [1-(1.062)^{-20}]}{0.062}[/tex]
i.e. [tex]PV=\frac{25312 \times [1-0.3003]}{0.062}[/tex]
i.e. [tex]PV=\frac{25312 \times 0.6997}{0.062}[/tex]
i.e. [tex]PV=\frac{17695.62}{0.062}[/tex]
i.e. [tex]PV=285,413.23[/tex]
Hence, the amount to be deposited at the start of the year is $285,413.23.
