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Help Solve this Case

Anonymous A

I recently had an interview with OW and was given this case. Needless to say, I did not solve it adequately. Can anyone help...? :

You are a new investmend fund and raised a mere $100, and you want to focus on retail/consumer lending. You're objective is to get a 20% return on your initial $100 capital via lending. You know that 90% of your customer base will pay back the full amount + interest. While 10% of your customers will default on their loan and pay only 20% in interest. What interest price should you charge in order to guarantee a 20% return on your $100?

Any help would be truly appreciated!

Aneesh Chandra Kumaran replied on 08/14/2017

This is how I would solve the problem.

Consider "x" as the interest to be charged.

We know that 90% of the clients will pay back full amount plus interest : 1+x

10% of the clients only pay 20% in interest : 0.2

For us to get 20% guaranteed return on investment, we should solve for the following equation

0.9(1+x) + 0.1(0.2) = 1.2 => x=0.311

So we should charge 31.11% interest.

Not sure if my approach is accurate but hope it helps.

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