The purpose of this article is to extend the mathematics of continuously compounded interest to include a very common application of compound interest: namely fixed-repayment loans more commonly referred to as mortgages or annuities. In the same way that it is possible to derive the formula for continuous compounding by taking to infinity the frequency (N) of compounding periods (N = 12 for monthly compounding), we can derive a formula for a 'continuous repayment mortgage'.

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dbpprop:abstract
  • The purpose of this article is to extend the mathematics of continuously compounded interest to include a very common application of compound interest: namely fixed-repayment loans more commonly referred to as mortgages or annuities. In the same way that it is possible to derive the formula for continuous compounding by taking to infinity the frequency (N) of compounding periods (N = 12 for monthly compounding), we can derive a formula for a 'continuous repayment mortgage'. In this article the derivation is presented and the result compared with a well known physical system which exhibits the same mathematical characteristics. The time continuous mortgage function obeys a first-order linear differential equation and an alternative derivation thereof is obtained by solving the equation using Laplace transforms.
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  • The purpose of this article is to extend the mathematics of continuously compounded interest to include a very common application of compound interest: namely fixed-repayment loans more commonly referred to as mortgages or annuities. In the same way that it is possible to derive the formula for continuous compounding by taking to infinity the frequency (N) of compounding periods (N = 12 for monthly compounding), we can derive a formula for a 'continuous repayment mortgage'.
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  • Continuous-repayment mortgage
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