Your firm has taken out a $549,000 loan with 8.1% apr (compounded monthly) for some commercial...

Your firm has taken out a $549,000 loan with 8.1% apr (compounded monthly) for some commercial property. as is common in commercial real estate the loan is a 5 year loan based on 15 year amortization. this means that your loan payments will be calculated as if you will take 15 years to pay off the loan, but you actually must do so in 5 years. to do this you will make 59 equal payments based on the 15 year amortization schedule and then make a final 60th payment to pay the remaining balance.

a. What will your monthly payments be?

b. What will your final payment be?

Expert Solution

This question is a classic example of a balloon mortgage. In order to solve this question, first we need to see the monthly payment schedule and the total balance at the end of 59 payments

Hence, we pay for 59 months, the ammortization cost over 15 years and the the 60th payment would be the balance amount.

Let's first calculate the monthly mortgage payment

Total Loan value = USD 549,000

Rate of interest = 8.1% ( compounded monthly)

Monthly rate of interest = 0.081/12 = 0.00675 which results in annualized interest rate of 8.4%

Ammortization duration = 15 years = 180 months

Monthly mortgage payment = USD 5,374

At the end of 59 months, total payment = 5374*59 = 317,066 USD

Balloon payment is the balance payment at the end of 59 months = 440,693.64 USD

Here's how the payment schedule looks like

vent	Loan	Payment	Interest	Principal	Balance
Loan 1	$549,000.00		$0.00	$0.00	$549,000.00
Payment 1		$5,374.09	$3,843.00	$1,531.09	$547,468.91
Payment 2		$5,374.09	$3,832.28	$1,541.81	$545,927.10
Payment 3		$5,374.09	$3,821.49	$1,552.60	$544,374.50
Payment 4		$5,374.09	$3,810.62	$1,563.47	$542,811.03
Payment 5		$5,374.09	$3,799.68	$1,574.41	$541,236.62
Payment 6		$5,374.09	$3,788.66	$1,585.43	$539,651.19
Payment 7		$5,374.09	$3,777.56	$1,596.53	$538,054.66
Payment 8		$5,374.09	$3,766.38	$1,607.71	$536,446.95
Payment 9		$5,374.09	$3,755.13	$1,618.96	$534,827.99
Payment 10		$5,374.09	$3,743.80	$1,630.29	$533,197.70
Payment 11		$5,374.09	$3,732.38	$1,641.71	$531,555.99
Payment 12		$5,374.09	$3,720.89	$1,653.20	$529,902.79
Payment 13		$5,374.09	$3,709.32	$1,664.77	$528,238.02
Payment 14		$5,374.09	$3,697.67	$1,676.42	$526,561.60
Payment 15		$5,374.09	$3,685.93	$1,688.16	$524,873.44
Payment 16		$5,374.09	$3,674.11	$1,699.98	$523,173.46
Payment 17		$5,374.09	$3,662.21	$1,711.88	$521,461.58
Payment 18		$5,374.09	$3,650.23	$1,723.86	$519,737.72
Payment 19		$5,374.09	$3,638.16	$1,735.93	$518,001.79
Payment 20		$5,374.09	$3,626.01	$1,748.08	$516,253.71
Payment 21		$5,374.09	$3,613.78	$1,760.31	$514,493.40
Payment 22		$5,374.09	$3,601.45	$1,772.64	$512,720.76
Payment 23		$5,374.09	$3,589.05	$1,785.04	$510,935.72
Payment 24		$5,374.09	$3,576.55	$1,797.54	$509,138.18
Payment 25		$5,374.09	$3,563.97	$1,810.12	$507,328.06
Payment 26		$5,374.09	$3,551.30	$1,822.79	$505,505.27
Payment 27		$5,374.09	$3,538.54	$1,835.55	$503,669.72
Payment 28		$5,374.09	$3,525.69	$1,848.40	$501,821.32
Payment 29		$5,374.09	$3,512.75	$1,861.34	$499,959.98
Payment 30		$5,374.09	$3,499.72	$1,874.37	$498,085.61
Payment 31		$5,374.09	$3,486.60	$1,887.49	$496,198.12
Payment 32		$5,374.09	$3,473.39	$1,900.70	$494,297.42
Payment 33		$5,374.09	$3,460.08	$1,914.01	$492,383.41
Payment 34		$5,374.09	$3,446.68	$1,927.41	$490,456.00
Payment 35		$5,374.09	$3,433.19	$1,940.90	$488,515.10
Payment 36		$5,374.09	$3,419.61	$1,954.48	$486,560.62
Payment 37		$5,374.09	$3,405.92	$1,968.17	$484,592.45
Payment 38		$5,374.09	$3,392.15	$1,981.94	$482,610.51
Payment 39		$5,374.09	$3,378.27	$1,995.82	$480,614.69
Payment 40		$5,374.09	$3,364.30	$2,009.79	$478,604.90
Payment 41		$5,374.09	$3,350.23	$2,023.86	$476,581.04
Payment 42		$5,374.09	$3,336.07	$2,038.02	$474,543.02
Payment 43		$5,374.09	$3,321.80	$2,052.29	$472,490.73
Payment 44		$5,374.09	$3,307.44	$2,066.65	$470,424.08
Payment 45		$5,374.09	$3,292.97	$2,081.12	$468,342.96
Payment 46		$5,374.09	$3,278.40	$2,095.69	$466,247.27
Payment 47		$5,374.09	$3,263.73	$2,110.36	$464,136.91
Payment 48		$5,374.09	$3,248.96	$2,125.13	$462,011.78
Payment 49		$5,374.09	$3,234.08	$2,140.01	$459,871.77
Payment 50		$5,374.09	$3,219.10	$2,154.99	$457,716.78
Payment 51		$5,374.09	$3,204.02	$2,170.07	$455,546.71
Payment 52		$5,374.09	$3,188.83	$2,185.26	$453,361.45
Payment 53		$5,374.09	$3,173.53	$2,200.56	$451,160.89
Payment 54		$5,374.09	$3,158.13	$2,215.96	$448,944.93
Payment 55		$5,374.09	$3,142.61	$2,231.48	$446,713.45
Payment 56		$5,374.09	$3,126.99	$2,247.10	$444,466.35
Payment 57		$5,374.09	$3,111.26	$2,262.83	$442,203.52
Payment 58		$5,374.09	$3,095.42	$2,278.67	$439,924.85
Payment 59		$5,374.09	$3,079.47	$2,294.62	$437,630.23
Balloon 1		$440,693.64	$3,063.41	$437,630.23	$0.00

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