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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

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abiolataiwo2015

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%.

Learn more about investment rate here:https://brainly.com/question/2294792

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