Worked solution · Exam FM
This Exam FM sample reference tests Equivalent Growing Annuities. The twenty increasing payments have present value 52732.61. In the thirty-payment due annuity, growth equals yield, so each discounted payment equals k and the value is 30k; hence k = 1757.75 and choice A.
Independent solution
Setup
Value the first annuity as a finite growing annuity-immediate.
Model
For the second annuity, each 4% payment increase exactly cancels one year's 4% discount.
Compute
Its thirty discounted payments therefore have value 30k.
Answer
The initial payment is approximately 1758, choice A.
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Error diagnosis
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Original practice · fully worked
A twelve-payment annuity-immediate begins with 1,000 and grows 3% annually. At a 5% effective yield, it is exchanged for a ten-payment level annuity-due. Determine the level annual payment.
The growing stream is worth 10304.15. Dividing by the ten-payment annuity-due factor at 5% gives a level payment of 1270.89, choice C.
Setup
Discount the twelve growing payments to the exchange date.
Model
The replacement stream begins immediately and has ten level payments.
Compute
Equate values and divide by the due factor.
Answer
The replacement payment is 1270.89, choice C.
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