Financial Math(20 points)

憂鬱的人

2009-11-01 3:53 am

Jason is securing a 7-year balloon mortgage for $280000 to finance the purchase of his first home. The monthly payments are based on a 30-year amortizaton. If the prevailing interest rate is 7.5%/year compounded monthly, what will be his balloon payment at the end of 7years?

Jason's monthly payment is $1957.80

更新1:

the answer is $257135.23

回答 (1)

用戶9112

2009-11-01 4:09 am

✔ 最佳答案

The monthly interest rate r = 7.5%/12 = 0.00625
The balance amount after 1 month
= 280000 * (1 + r) - 1957.8
The balance amount after 2 months
= [280000 * (1 + r) - 1957.8](1 + r) - 1957.8
= 280000 * (1 + r)^2 - [1957.8(1 + r) + 1957.8]
The balance amount after 3 months
= [280000 * (1 + r)^2 - [1957.8(1 + r) + 1957.8]](1 + r) - 1957.8
= 280000 * (1 + r)^3 - [1957.8(1 + r)^2 + 1957.8(1 + r) + 1957.8]
= 280000 * (1 + r)^3 - 1957.8[(1 + r)^3 - 1]/r
The balance amount after 7 years (84 months)
= 280000 * (1 + r)^84 - 1957.8[(1 + r)^84) - 1]/r
= 472555.77 - 215420.40
= 257135.37

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