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The purchase price of a property is $195,000. What are the required monthly repayments for the following mortgage packages 1) An initial downpayment of 20% of the purchase price and a 30-yr fixed APR of 3.375%. 2) An intital downpayment of 10% of the purchase price and a 15-yr fixed APR of 2.625%.

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The purchase price of the property is $195,000.

1) If a downpayment of 20% is made, then the borrowed amount will be

0.8 x 195000 = 156000.

At a 30-yr fixed interest rate of 3.375% APR on the remaining total unpaid, in the ith year the total will reduce to

`T_i = 1.03375T_(i-1) - 12m`

where `m` is the monthly repayment.

Using a simple recursive program and refining our answer by trial and error (eg bifurcation), we find that, to pay the mortgage off in the 30 years planned, the required monthly repayment will be m = $695.80.

2) If a downpayment of 10% is made, the n the borrowed amount will be

0.9 x 195000 = 175500.

At a 15-yr fixed interest rate of 2.625% APR on the remaining total unpaid, in the ith year the total will reduce to

`T_i = 1.02625T_(i-1) - 12m`

Again using a simple recursive progam and refining our answer by trial and error, we find that, to pay the mortgage off in the 15 years planned, the required monthly repayment will be m = $1192.10

For mortgage 1) the required monthly repayment is $695.80. For mortgage 2) the required monthly repayment is $1192.10.

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