Interest Rate

A certain UK supmarket has a Xmas Saving Card. One puts money on it throughout the year and around November a bonus is added depend on how much has been saved. For example, saving the maximum of £280 earns a £15 bonus.

We can easily see this is a very good rate of interest as £15 on and investment of £280 over and entire year would be over 7.2%. However, one can save £50 per month for 5 months + £30 for one month and still earn the same bonus. If one were to do that, starting in April, is there a simple formula for calculating the effective rate of interest?

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ElwoodBlues · M

What you're asking for is known as the "internal rate of return" of cash flows and you can find some online calculators for it.

This one here assumes all monthly payments are the same.
https://cccpa.com/internal-rate-of-return-irr-calculator/

This one here might do it for you.
https://vindeep.com/Calculators/IRRCalculator.aspx

If you have access to an Excel spreadsheet, I believe Excel can do it for an arbitrary series of payments.

rob19 · M

@ElwoodBlues Thanks for that. I'm more interested in a formula for calulating it. Knowing it's the "internal rate of return" is a help though.

ElwoodBlues · M

@rob19 In the general case you can't solve analytically for IRR, but if you use numerical methods, gradient descent should work.