Dear all need a little help with this, l cant get it no matter how l calculate, l may be understanding the question wrong :((

Mr A wants to retire in 30 years, and he would like to have an annuity of $1000/yr for the next 20 years after retirement.

Using an interest rate of 10% per annum, how much must he invest today (present value ? ) in order to have his retirement annuity?

Please advise

Thank you

If u draw a time-line with 50 years, he must invest some money today at an annual rate of 10% to give him some amount at 30 years that can remain invested to give him an annual annuity over the next twenty years that pays $1000 per year.. So, I'd start by working backwards with the annuity. You know the payment is $1k per year, the interest rate is 10% per year & the time frame is 20 years, just plug the values into the annuity formula (below) & u will arrive at the present value of that annuity. The twist to this problem is that the present value of that annuity is 30 years down the road, so it is also the future value of the investment he must make today. Since u know this future value (aka the PV of the annuity in 30 years) of his investment today, the time frame (30 years) & the annual interest rate (10%), u can solve for the present value of the investment with the PV formula (below)

Annuity --- payment((1/r)-(1/(r(1+r)^t)))
1000 * ((1/.1)-(1/(.1*(1+.1)^20))) = 8513

8513 is the value of the annuity at the beginning of the 20 years of retirement, so, it is the value he needs to work toward with his investment today..

PV of 8513 ---- PV = FV/(1+r)^t
--- PV = 8513/(1+.1)^30 = 487.9

l believe this is what u r looking for..

Hope this helps, best of luck