# Looking for a Formula for ROI, couldn't get an answer in Finance

This is honestly a pretty simple problem, but for whatever reason I am not able to pull it all together. I was talking theoretically with a friend and neither of us can nail down the maths so I coming to the internet for help.

You are loaning out money with a $10\%$ interest rate and starting with a $300,000$ loan. So every month you are receiving $\frac{330,000}{12}= 27500$. Every $3$ months you loan out all your money received. So if the $300,000$ loan was sent out on $Jan- 1$, year $1$, then an $27500\times3= 82500$ loan is leant out on April $1$, year $1$. This continues, but after $12$ months of payments you stop receiving the $27500$ a month since the loan is now fully paid back.

I figured if you stop reinvesting after $9$ months you'd make ~$360k$ after all loans are paid back and after $45$ months you would make ~$630k$ after everything is paid back. I think the first number is right but the second one is really wrong. Is there a formula I'm forgetting from an Econ $101$ class that I could use to solve this problem? We are hoping to get the total you would earn if you were to stop reinvesting during any quarter.

• It's a flat 10% on the total loan, paid back in 12 equal segments. – Rob Aug 13 '15 at 20:43