I was looking over different payment schemes for insurance to decide which was best. I wrote out a simple equation to find the effective interest rate that each charges to accept payments.(adsbygoogle = window.adsbygoogle || []).push({});

I'm not explaining myself well; let me make this more concrete. Suppose you could pay $1000 at the beginning of the year, or make two payments of $520 on Jan 1 and Jul 1. For these deals to be equal, you'd need to make $40 of interest on $480 over six months. The effective monthly rate is such that

[tex]\left(1+\frac{r}{12}\right)^6=\frac{520}{480}[/tex]

and so

[tex]r=12\left(\frac{520}{480}\right)^{1/6}-12\approx16.11\%.[/tex]

Unfortunately, my equation didn't work. I thought to solve this in two steps:

1. Given p payments of $b, find an r such that the annual rate $A = $b + $b * r + $b * r^2 + ... + $b * r^{p-1}.

2. With this r, calculate the interest rate as

[tex]\frac{12}{p}\left(r^{-p/12}-1\right)[/tex]

It looks like I'm doing #1 wrong, because my numbers don't match my double-check spreadsheet (where I calculated the interest rate by 'manual binary splitting' = glorified trial and error). But the process is so simple () that I don't know where I'm going wrong!

I'm using a numerical solver to find an r in [0.7, 0.99] (corresponding to an interest rate of 1% to 43%, which the spreadsheet shows as reasonable) such that

[tex]A-b\frac{1-r^p}{1-r}=0[/tex]

since b + br + ... br^{p-1} is [itex]b\frac{1-r^p}{1-r}.[/itex] What am I doing wrong?

**Physics Forums - The Fusion of Science and Community**

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

# Effective rate (making dumb mistakes)

Loading...

Similar Threads - Effective rate making | Date |
---|---|

B Complex products: perpendicular vectors and rotation effects | Dec 17, 2017 |

I Does this scatter chart really show a cause and effect? | Apr 17, 2017 |

Effective annual return rate and the annual percentage return rate | Nov 3, 2014 |

The undone effect/inverse. Multiply to divide, plus to minus | May 18, 2014 |

How to work out the effective annual rate if you ocmpound 6% nominal for indefinite | Nov 23, 2006 |

**Physics Forums - The Fusion of Science and Community**