Some "Payday Loan Companies" have added a new service where they offer people who have guaranteed monthly pensions, like veterans, a lump sum of money in lieu of their regular monthly payments. The pensioner receives this one-time amount, minus processing fees, from the loan company, which then collects his future monthly pension checks in repayment for this "loan.“ GI Joe is single and receiving a $3,000 monthly pension for the rest of his life, estimated to be 30 more years. He needs cash right now, so he is considering a contract where the El Stinko Loan Company (ESL) gives him a one-time, lump sum amount of $156,125 right now. In return, GI Joe has the Veteran's Administration send all of his future monthly $3,000 checks, starting the end of this month, directly to ESL in repayment of this "loan." Joe also has to pay a processing fee of 4% of the lump sum amount of $156,125 so he is only receiving $149,880. Assuming Joe does live for exactly 30 more years, what APR rate is ESL earning on their investment of $149,880 in Joe? Asked another way, what APR rate is GI Joe paying for this loan?
Suppose Joe accepted the arrangement from ESL, happily used his lump sum amount for sex, booze and drugs, and as a result, died after 10 years instead of living out his expected 30 years. Veteran's Benefits stop at death with no survivors. Hence, ESL would only receive 120 months of Joe's $3,000 pension in repayment for the "loan" of $149,880 instead of the expected 360 months of pension. What APR rate would ESL earn on this revised investment of receiving just 120 months of $3,000 in return for a "loan" of $149,880? (if you use the compound interest table to solve, it's OK to do a little rounding here) Are you sorry for ESL? (Note that the rates you calculated in 8a and 8b are “Fee-inclusive” interest rate, since they were calculated on the balance of $149,890 after deducting the 4% in fees.)