Question

As part of your retirement plan, you want to set up an annuity in which a regular payment of $25,312 is made at the end of each year. You need to determine how much money must be deposited earning 6.2% compounded yearly in order to make the annuity payment for 20 years.

Answer 1

Answer:

$285,413.23

Step-by-step explanation:

We know the annuity formula is given by,

$P=\frac{r \times PV}{1-(1+r)^{-n}}$,

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,

$PV=\frac{25312 \times [1-(1+0.062)^{-20}]}{0.062}$

i.e. $PV=\frac{25312 \times [1-(1.062)^{-20}]}{0.062}$

i.e. $PV=\frac{25312 \times [1-0.3003]}{0.062}$

i.e. $PV=\frac{25312 \times 0.6997}{0.062}$

i.e. $PV=\frac{17695.62}{0.062}$

i.e. $PV=285,413.23$

Hence, the amount to be deposited at the start of the year is $285,413.23.