1 Remaining: 96 mi I Back to Score: /6 oblem 5.35 rtization schedule with a ball
ID: 2793556 • Letter: 1
Question
1 Remaining: 96 mi I Back to Score: /6 oblem 5.35 rtization schedule with a balloon payment want to buy a house that costs $180,000. You have $18,000 for a down payment, but your credit is such that mortgage companies will not lend you the required $162,000 2,000 mortgage (called a seller take-back mortgage) at a rate of 5%, provided the loan is paid off in full in 3 years. You expect to inherit $180,000 in 3 years; but right now ments of no more than18,000 per year given your salary·(The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.) a. If the loan amortized over 3 years, how large would each annual payment be? Round your answer to the nearest cent. Could you afford those payments? b. If the loan were amortized over 30 years, what would each payment be? Round your answer to the nearest cent Could you afford those To satisfy the seller, the 30-year mortgage loan would be written as a balloon note, which means that at the end of the third year, you would have to make the regular payn c. What would the loan balance be at the end of Year 3? Round your answer to the nearest cent. What would the balloon payment be? Round your answer to the nearest cent.Explanation / Answer
A
Loan Amount = $162000
Amortization period = 3 years
Rate of interest = 5%
Payments will be made monthly but in the question we've been asked to calculate one annual payment.
Annual Payment = Loan amount * Annual Interest rate/ ( 1 – (1+ Annual Interest Rate)^-number of payments)
= $162000 * 0.05 /(1-(1.05)^-3) = $59487.79
You will not be able to pay this amount as you have a budget constraint which limits your paying ability to $18000 annually
B
Same formula will be used to calculate annual payment over amortization period of 30 years
Loan Amount = $162000
Amortization period = 30 years
Rate of interest = 5%
Annual Payment = Loan amount * Annual Interest rate/ ( 1 – (1+ Annual Interest Rate)^-number of payments)
= $162000 * 0.05 /(1-(1.05)^-30) = $10538.33
This amount is well within your budget of $18000
C
Loan Amount = $162000
Amortization period = 30 years
Rate of interest = 5%
Annual Payment = Loan amount * Annual Interest rate/ ( 1 – (1+ Annual Interest Rate)^-numbers of payments)
= $162000 * 0.05 /(1-(1.05)^-30) = $10538.33
Amortization Schedule
Year
Payment
Interest
Principal
Balance
0
$162000
1
$10538.33
$8100
$2438.33
$159561.67
2
$10538.33
$7978.0835
$2560.2465
$157001.4235
3
$10538.33
$7850.071175
$2688.258825
$154313.1647
Balance at the end of third year = $154313.16 = Balloon Payment
Loan balance will become 0 after you’ve paid off the Balloon Payment.
Year
Payment
Interest
Principal
Balance
0
$162000
1
$10538.33
$8100
$2438.33
$159561.67
2
$10538.33
$7978.0835
$2560.2465
$157001.4235
3
$10538.33
$7850.071175
$2688.258825
$154313.1647
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