Loaned out $10K, with the following payments (like, these are all the payments there will ever be)
Period 1 2 3 4 5 6 $0 $0 $0 $0 $26K $4K
How would I calculate the interest rate?
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One method: set up a spreadsheet with a cell labelled "rate", and columns labelled "balance" and "payments". Enter the payments, initialize the first balance as 10,000, then set each subsequent balance as the previous balance plus the previous balance times the rate minus the payment. Now go to "goal seek"/"solver", and find the rate that sets the final balance to zero. Depending on the timing of the payments, you may need to add in another period. For instance, if the nth payment is made after n years, then you should start you sheet at period 0 so that interest has accrued by period 1.
Let's call the interest rate
After one year, you owe
10*(1+r), after two years
10*(1+r)^2, etc, then after 5 years, you owe
10*(1+r)^5-26, and finally after 6 years
(10*(1+r)^5-26)*(1+r)-4 - which is
You can now solve the equation for