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 $7,900.00 today and then will be paid a 8.00% 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 25.00 more years after your 65th birthday. The former student wants a return of 8.00% on his investments, but would like to consider this opportunity.

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

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Answer format: Currency: Round to: 2 decimal places.

Answer 1

Answer:

Annuity (A) = APR * Investment

       = 8% * 7,900 = $632

The former student is currently on his 50th birthday. First payment comes on 65th birthday which is 15 years away from today and the last payment comes 25 years after his 65th birthday that is 25+15 = 40 years from today

Desired return, r = 8%

Hence, value of these annuity today = PV of all the future annuities = A /(1+r) ^15 + A / (1+r) ^16 + ....A / (1+r) ^40

= A /(1+r)^15 * (1- (1+r)^-25 / 1 – (1+r) ^-1)

= 632/(1+0.08)^15 * (1- (1+0.08)^-25/ 1- (1+0.08) ^-1)

= 199.2327 * 0.85398209508/0.07407407407

= 199.2327 * 11.5287582842

= 2296.90564061

= $2,296.90

The value of this deferred annuity today on his 50th birthday is $2,296.90