Find the unpaid balance on the debt. (Round your answer to the nearest cent.) Af

Question

Find the unpaid balance on the debt. (Round your answer to the nearest cent.)

After 5 years of monthly payments on $140,000 at 5% for 25 years.

$ ___________

The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 20 years. If the prize money is guaranteed by AAA bonds yielding 6% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.) $ ____________

Explanation / Answer

Answer 1.

Amount of Debt = $140,000
Annual Interest Rate = 5%
Monthly Interest Rate = 5%/12 = 0.4167%
Period of Debt = 25 years or 300 months

Monthly Payment = $140,000 / PVA of $1 (0.4167%, 300)

PVA of $1 (0.4167%, 300) = (1 - (1/1.004167)^300) / 0.004167
PVA of $1 (0.4167%, 300) = 171.05323

Monthly Payment = $140,000 / 171.05323
Monthly Payment = $818.46

Balance of Debt after 5 years = $818.46 * PVA of $1 (0.4167%, 240)
Balance of Debt after 5 years = $818.46 * (1 - (1/1.004167)^240) / 0.004167
Balance of Debt after 5 years = $818.46 * 151.52024
Balance of Debt after 5 years = $124,013.26

So, balance after 5 years of monthly payments is $124,013.26

Answer 2.

Super Prize = $10,000,000
Super prize is paid in 20 equal annual payments
Annual Payments = $10,000,000 / 20
Annual Payments = $500,000

Prize money is guarantee by AAA bond yielding 6%

Amount deposited in Escrow Account = $500,000 * PVA of $1 (6%, 20)
Amount deposited in Escrow Account = $500,000 * (1 - (1/1.06)^20) / 0.06
Amount deposited in Escrow Account = $500,000 * 11.46992
Amount deposited in Escrow Account = $5,734,960

So, amount deposited into an escrow account is $5,734,960

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