Does anyone know how I can work out a formula to calculate how long it will take to pay a loan back to zero if the interest is on a loan is calculated daily but compounded at the end of the month. To add another level of complexity, assume you are making fortnightly repayments.(adsbygoogle = window.adsbygoogle || []).push({});

P (Principal) = $500,000

E (Fortnightly Repayments) = $2,500

r (annual interest rate) = 8.59%

t (daily compound interest rate) = [tex]\frac {0.0859}{365}[/tex]

I started out with the following:

[tex] A_0 = P[/tex]

[tex] A_1_4 = P-E[/tex]

[tex] A_2_8 = P-2E[/tex]

[tex] A_3_0 = A_2_8 + 14(A_0 * t) + 14(A_1_4 * t) + 2(A_2_8 * t) [/tex]

[tex]= P - 2E + 14(Pt) + 14(Pt-Et) + 2(Pt-2Et)[/tex]

[tex]= P-2E+30Pt-18Et[/tex]

and continuing...

[tex]A_4_2 = A_3_0 - E = P-3E+30Pt-18Et[/tex]

[tex]A_5_6 = A_4_2 - E = P-4E+30Pt-18Et[/tex]

[tex]A_6_0 = A_5_6 + 12(A_3_0 * t) + 14(A_4_2 * t) + 4(A_5_6 * t)[/tex]

[tex]A_1_4[/tex] and [tex]A_2_8[/tex] is where I make repayments. [tex]A_3_0[/tex] is where the interest is finally compounded.

Am I heading in the right direction for this?

Can anyone enlighten me on the best way to go about solving this?

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# Interest calculated daily compounded monthly

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