Question

A University is offering a charitable gift program. A former student who is now 50 years old is consider the following offer: The student can invest $7,600.00 today and then will be paid a 9.00% APR return starting on his 65th birthday (i.e For a $10,000 investment, a 9% rate would mean $900 per year). The program will pay the cash flow for this investment while you are still alive. You anticipate living 22.00 more years after your 65th birthday. The former student wants a return of 6.00% on his investments, but would like to consider this opportunity.

What is the annual cash flow from the investment starting on the student's 65th birthday?

Using the student's desired return, what is the value of this deferred annuity today on his 50th birthday?

Answer 1

Annual cash flow on investment starting from 65th Birthday = 7600 * 9 % = 684

This cash flow is expected to receive for 22 years

Present value of 22 cash flows (When the student turns 64 years)

N = 22

PMT = 684

IY = 6

FV = 0

Compute PV we get 8236.44

Now we need to find the present value after 50 th birthday, i.e discount further by 14 years

PV = FV / (1+R)^N

PV = 8236.44 / (1+6%)^14

PV = 3642.99

The value of deferred annuity as per the desired return is 3642.99