Question

Suppose you are offered an investment opportunity that will pay you $3136.72 per month for 49 months. To make this investment, you must invest a total of $125000, but only $12500 is in cash at the start. You must borrow the rest of the investment ($112500) from Lo-Rate Bank at 14.6% APR, with monthly compounding, and the entire loan must be repaid at the end of the 49 months in one lump sum, which will total $203470.77. To be clear, absolutely NO repayment of the loan before the end of the 49 months is allowed. This investment is completely riskless and there are no taxes. What is the minimum APY you would need to be able to earn from reinvesting all the monthly income to make this a zero-NPV investment? (Percent with 2 decimals.)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

в с D Initial Payment Monthly amount receipt No. of month Last month payment $12,500.00 $3,136.72 49 $203,470.77 -Nm tooooo Monthly Internal rate of return 1.60% Minimum APY to get Zero-NPV 20.98% 11

Cell reference -

B 12500 3136.72 Initial Payment Monthly amount receipt No. of month Last month payment 49 203470.77 M70 Monthly Internal rate of return =RATE(C4,-C3,C2,C5,0) Minimum APY to get Zero-NPV =(1+C7)^12-1 10 11 12

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.