Question

An ordinary annuity selling at $9,697.45 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity's appropriate interest rate (1) remains at 8.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $85,000,000, paid in eight equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won assuming an annual interest rate of 8.00%. $122,055,302.037 $65,942,681.88 $61,058,038.78 $113,014,168.553 David needed money for some unexpected expenses, so he borrowed $5,464.40 from a friend and agreed to repay the loan in eight equal installments of $1,100 at the end of each year. The agreement is offering an implied interest rate of David's friend, Keanu, has hired a financial planner for advice on retirement. Considering Keanu's current expenses and expected future lifestyle changes, the financial planner has stated that once Keanu crosses a threshold of $4,991,331 in savings, he will have enough money for retirement. Keanu has nothing saved for his retirement yet, so he plans to start depositing $85,000 in a retirement fund at a fixed rate of 12.00% at the end of each year. It will take years for Keanu to reach his retirement goal

Answer 1

Present Value of payments = $9,697.45

Time Period = 8 years

Interest Rate = 8%

Let the annual payments be x

9,697.45 = x*PVAF(8%, 8 years)

9,697.45 = x*5.747

X = $1,687.39 (approx.)

Hence, the annual annuity payment will be $1,687.39

Annual payment = $85,000,000/8 = $10,625,000

Since first payment is made today, it is already at its present value

Present Value of payments = $10,625,000 + 10,625,000*PVAF(8%, 7 years)

= 10,625,000 + 10,625,000*5.206

= $65,938,750

Or $65,942,681.88 (approx)

Let the interest rate be x%

5,464.40 = 1,100*PVAF(x%, 8 years)

PVAF(x%, 8 years) = 4.9676

From Present Value annuity factor table, x = 12%

Hence, implied interest rate = 12%

Let it takes x years

4,991,331 = 85,000[{(1+0.12)^x – 1}/0.12]

8.04658 = (1.12)^x

X = 19 years (approx.)