Mary Jo wants to buy a boat that is available at two dealerships. The price of the boat is the same at both dealerships. Middlefield Motors would let her make quarterly payments of 4,827.66 dollars for 8 years at a quarterly interest rate of 2.35 percent. Her first payment to Middlefield Motors would be due immediately. If Fairfax Boats would let her make equal monthly payments of 2,608 for 4 years and if her first payment to Fairfax Boats would be in 1 month, then what is the monthly interest rate that Mary Jo would be charged by Fairfax Boats? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.
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1. For deal from Middlefield Motors, First installment is due today , so PV of rest 31 installments dsicounted @ 2.35% (since this is the quarterly intrest itself) for 31 period (8*4-1, since the first one is due today- gives = PV (2.35%,31, 4827.66) =105444.88, Add to it the current 1st installment due today to get the PV of the boat = 105444.88+ 4827.66= 110272.54
Now with this PV and 48 period installment (4*12 monthly installment) and 2608 per month we can find monthly rate easily, ie = RATE (48, 2608, -110272.54) = 0.53% (-110272.54Because that is how the formula adjusts it).
So monthly rate by fairfax is 0.53% = 0.0053
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