Question

# Jessica has just won a lottery jackpot. She will get the money in 26 equal installments...

Jessica has just won a lottery jackpot. She will get the money in 26 equal installments of \$307,692 each, starting immediately. The Li Li Finance Company offers her \$2,000,000 cash if she signs the payments over to them. What interest is the Li Li Finance Company earning on this offer?

a.5.5%

b.7.5%

c.7.8%

d.17.9%

e.15%

Present Value of annuity = P * [ (1 - ( 1 + r)^-n) / r)] * (1 + r)

Where, P is Payment

r = rate per period

n = Number of period

200,000 = 307692 [ (1 - ( 1 +r)^-26) / r] * (1 + r)

200,000 / 307692 = [ (1 - ( 1 +r)^-26) / r] * (1 + r)

6.50 = (1 - (1+r)^-26)/r * * (1 + r)

We will use hit and trial method

First, We will try for 10%

6.50 = [( 1 - (1+10%)-26)] / 0.10 * (1 + 0.10)

6.50 = (1 - 0.083) / 0.10 * (1.10)

6.50 = 9.160 * (1.10)

6.50 = 10.076

At 10%, The value of right hand side is higher so we will try higher discount rate,So, Options A,B,C are wrong.

At 17.9%

6.50 = [( 1 - (1+17.9%)-26)] / 0.179 * (1 + 0.179)

6.50 = 5.50936 * (1.179)

6.50 = 6.50

So, At 17.9%, The Both sides are equal, Thus Option D is the correct answer

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