interest
2011-11-28 5:27 pm
A man takes out a mortgagefor $20,000 for 25 years. If the rate of interest is 12%, what is the annualmortgage payment?Find the annual mortgage paymentsfor a 20-year mortgage of $25,000 if the rate of interest is :i) 10%;ii) 15%.
回答 (1)
2011-12-03 1:05 am
✔ 最佳答案
1) Let $p be the annual payment, then:After 1st year, amount left = 20000 x 1.12 - p
After 2nd year, amount left = (20000 x 1.12 - p) x 1.12 - p
= 20000 x 1.122 - 1.12p - p
After 25 years, amount left is:
20000 x 1.1225 - (1.1224 + 1.1223 + ... + 1)p
= 20000 x 1.1225 - (1.1225 - 1)p/(0.12)
which should be 0, i.e.
(1.1225 - 1)p/(0.12) = 20000 x 1.1225
p = 2550
2 i) Let $p be the annual payment, then:
After 1st year, amount left = 25000 x 1.1 - p
After 2nd year, amount left = (25000 x 1.1 - p) x 1.1 - p
= 25000 x 1.12 - 1.1p - p
After 20 years, amount left is:
25000 x 1.120 - (1.119 + 1.118 + ... + 1)p
= 25000 x 1.120 - (1.120 - 1)p/(0.1)
which should be 0, i.e.
(1.120 - 1)p/(0.1) = 25000 x 1.120
p = 2936
ii) Let $p be the annual payment, then:
After 1st year, amount left = 25000 x 1.15 - p
After 2nd year, amount left = (25000 x 1.15 - p) x 1.15 - p
= 25000 x 1.152 - 1.15p - p
After 20 years, amount left is:
25000 x 1.1520 - (1.1519 + 1.1518 + ... + 1)p
= 25000 x 1.1520 - (1.1520 - 1)p/(0.15)
which should be 0, i.e.
(1.1520 - 1)p/(0.15) = 25000 x 1.1520
p = 3994
參考: 原創答案
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