A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement

If the first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The investment rate the trust must earn to break even on this arrangement is: 5.56%.

Investment rate earn to breakeven

Given data:

Initial deposit = $2,000,000

Annual payment = $150,000

Number of years = 25 years

Using this formula to find the interest rate on the annuity by solving for I:

PV=PMT×1−(1+I)−^N/I

Where:

Present value (PV) = -2,000,000

Number of years (N) = 25

Periodic payment (PMT) =-150,000

Future value=0

Interest rate=I/Y = ?

Hence,

$2,000,000=$150,000×1−(1+I)−^25/I

Using a financial calculator to find interest rate(I/Y ) by inputting the below data

N = 25

I/Y = ?

PV = 2,000,000

PMT = -150,000

FV = 0

Hence,

CPT I/Y = 5.56%

Therefore If the first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The investment rate the trust must earn to break even on this arrangement is: 5.56%.

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