Question

Sally wants to set up a perpetual annuity for herself that Will pay 75,000 annually that will begin 40 years from now. Assuming an interest rate of 8% and with the impact of inflation of 3%. How much will Sally need to save annually?

3, 413

4415

5790

6419

Answer 1

Ans:- In this question, we need to find how much sally needs to save annually. This is a problem of growing perpetuity.

Now first we need to find the PV of growing Perpetuity.

PV of growing perpetuity is given by PMT / ( i - g) where PMT is Periodic annual Payments, i is the interest rate and g is the growth rate or inflation rate.

= $75,000 / ( 0.08 - 0.03)

= $1,500,000.

Now, this value must be equal to the Future Value of the Payments i.e P * [{(1+r)^n -1}/r], where P is the Periodic Payments, r is the rate per period, number of periods.

P*[{(1+r)^n -1}/r] = $1,500,000

P * [{( 1 + 0.08)^40 -1}/0.08] = $1,500,000

P * 259.057 = $1,500,000

or P = $1,500,000 / 259.057 = $5790.24. (approx).

Therefore the required amount that sally needs to save annually is $5790.24 that means the option (c) is the right answer.