# Looking for an ROI formula, brain is broken today

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 math 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 (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*3)= \$82500 loan is leant out on Apr1, 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 pad back. I think the first number is right but the second one is really wrong. Is there a formula I'm forgetting from an Econ101 class that I could use to solve this problem? We would just like to know how your money would look if you stop reinvesting at different years and how long would it take until you've hit a break even point (aka playing with house money).

• If you don't get an answer here, I'd suggest math.stackexchange.com – BobbyScon Aug 12 '15 at 22:07
• The suggested repayment schedule (\$27500 a month for 12 months on a \$300000 loan) represents an interest rate of over 19% a year, compounded monthly) – DJohnM Aug 13 '15 at 0:11

The monthly repayments of the initial \$ 300,000 loan can be calculated using this formula: source: Finance Formulas

``````pv = \$ 300,000
r = 0.10/12 per month
n = 12 months
``````

The monthly payment is

``````p = (r * pv)/(1 - (1 + r)^-n) = \$ 26,374.77
``````

It is not readily apparent how the formula works, but it is derived by induction from this summation, in which the sum of the discounted future payments are set equal to the present value of the loan: For the second part of the question, reinvestments are stopped after 9 months, after four investments of `\$ 26,374.77 * 3 = \$ 79,124.31`. And presumably each loan is repaid in 3 years, since 45 - 9 = 36 months.

Calculating the repayments for these loans:

``````pv = \$ 79,124.31
r = 0.1/12
n = 36

p = (r * pv)/(1 - (1 + r)^-n) = \$ 2,553.12

Total returned = 36 * \$ 2,553.12 = \$ 91,912.32
``````

The total returned for all four loans is:

``````\$ 91,912.32 * 4 = \$ 367,649.28
``````