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March 29, 2024, 11:21:00 pm

Author Topic: loan repayment and compounding question  (Read 667 times)  Share 

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thatdumbstudent

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loan repayment and compounding question
« on: April 24, 2020, 02:31:12 pm »
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I am stuck and honestly don't know how to tackle this at all :(

if you were to borrow $600,000 to borrow money for a house, over 20 years, at an interest rate of 3.7% compounding annually with fortnightly repayments, what would be your fortnightly repayment? I tried using the compound interest formula but the answer seems off ...

S_R_K

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Re: loan repayment and compounding question
« Reply #1 on: April 24, 2020, 04:26:23 pm »
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I am stuck and honestly don't know how to tackle this at all :(

if you were to borrow $600,000 to borrow money for a house, over 20 years, at an interest rate of 3.7% compounding annually with fortnightly repayments, what would be your fortnightly repayment? I tried using the compound interest formula but the answer seems off ...

How did you attempt to use the compound interest formula for this?

The compound interest formula won't work due to the fortnightly repayments, because each repayment adjusts the balance "directly", which thereby reduces the amount of interest added to the balance over the next fortnight, and so on. Note that this process is different from, first, calculating the total amount of debt that is built up over 20 years with a principal of $600 000 with 3.7% p.a. compounding fortnightly then, secondly, calculating the fortnightly repayment by dividing that total debt by 20*26.

This question is best done using a TVM solver on CAS.

plato

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Re: loan repayment and compounding question
« Reply #2 on: April 24, 2020, 11:48:23 pm »
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This question is beyond the scope of the curriculum. In Further Mathematics, the compounding and repayment periods are always equal.

S_R_K

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Re: loan repayment and compounding question
« Reply #3 on: April 25, 2020, 09:16:27 am »
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This question is beyond the scope of the curriculum. In Further Mathematics, the compounding and repayment periods are always equal.

Right, I missed that those periods aren't the same length.

With respect to it being in the course or not, when the new study design was introduced the advice was that compounding and repayment periods would initially be the same length, but in future years students might be expected to handle cases where they aren't. TVM solvers on CAS can easily handle the case where they aren't the same length.