1.The super prize in a contest is $10 million. This prize will be paid out in eq

Question

1.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 5% 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.)
$

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

After 6 years of monthly payments on $180,000 at 5% for 25 years.

3.Determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Quarterly payments on $16,500 at 3.2% for 6 years.

4. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)

Monthly payments on $170,000 at 5% for 25 years.

5.Calculate the present value of the annuity. (Round your answer to the nearest cent.)

$19,000 annually at 5% for 10 years.

Explanation / Answer

2) we have An = R * ( 1 - ( 1+ i) ^-n) / i

n = 12 * 25 = 300

i = 0.05/12 = 0.0042

so for An = 180000

180000 =  R * ( 1 - ( (1+ 0.0042) ^-300)) / 0.0042

R = monthly payment = $ 1056.46

After 6 years

number of payments left = n- k = (12*25) - (12*6) = 228

so to calculate unpaid balance

we use the expression

An-k =  R * ( 1 - ( 1+ i) ^-(n - k) ) / i

A n-k = 1056.46 * ( 1 - ( 1+ 0.0042) ^-(228) ) / 0.0042

Unpaid balance = A n-k = $ 154800.724 is the answer

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