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

506,240

Explanation:

Answer 2

$285,413.23

Explanation:

We know the annuity formula is given by,

`P=(r * 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=(25312 * [1-(1+0.062)^(-20)])/(0.062)`

i.e.
`PV=(25312 * [1-(1.062)^(-20)])/(0.062)`

i.e.
`PV=(25312 * [1-0.3003])/(0.062)`

i.e.
`PV=(25312 * 0.6997)/(0.062)`

i.e.
`PV=(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.