A state has a pension fund liability of $25 billion, due in 10 years. Each year

Question

A state has a pension fund liability of $25 billion, due in 10 years. Each year the Legislature is supposed to set aside an annuity to arrive at this future value. The annuity is based on the rate of return estimates.

a. Estimate the annuity needed each year for the next 10 years, assuming that the interest rate that can be earned on the money is 6%.

b. Assume the investment rate is revised to 8%. Recalculate the annuity needed to arrive at the future value.

c. Can the state take the difference between the two amounts as budget savings this year?

Explanation / Answer

Future Value (FV)=25 billion
Time period (n) =10 years
Part a.
R = 6%

Annuity payment= FV / FVIFA(10, 6%)
=25/13.1808
Annuity amount = $1.896698 billion

Part b.
R = 8%

Annuity payment = FV / FVIFA (10, 8%)
= 25/ 14.4866
Annuity amount = $1.725733 billion

Part c. Difference amount = $1.896698 - $1.725733=$0.170965 billion

If the rate of return is 8% then there will be saving of $0.170965 billion

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