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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Interest calculated daily compounded monthly

**Physics Forums | Science Articles, Homework Help, Discussion**