Question

Challenge question I.   Michael is shopping for a special automobile. He finds the exact car he wants, a 1966 dark blue Pontiac GTO. This car is currently the property of a neighbor, so to buy it for the agreed-upon price of $45,000, Michael must secure his own financing. He visits four different financial institutions and gets the following available loans:

Bank 1: 72 monthly payments of $767.21

Bank 2: 36 monthly payments of $1,404.95

Bank 3: 260 weekly payments of $206.46 (Assume a 52-week year.)

Bank 4: 16 quarterly payments of $3,281.53

Solve for all the banks.

Which loan should Michael take?  Hint:  Which loan has the lowest EAR?

If Michael selects Bank 1 for the loan, what is the periodic interest rate on the loan? (round to 4 decimals)

Answer 1

Periodic rate for Bank 1=RATE(72,-767.21,45000)=0.5834%

Annual rate or APR for Bank 1=0.5834%*12=7.0002%

EAR for Bank 1=(1+0.5834%)^12-1=7.2299%

Periodic rate for Bank 2=RATE(36,-1404.95,45000)=0.6458%

Annual rate or APR for Bank 2=0.6458%*12=7.7499%

EAR for Bank 2=(1+0.6458%)^12-1=8.0309%

Periodic rate for Bank 3=RATE(260,-206.46,45000)=0.1394%

Annual rate or APR for Bank 3=0.1394%*52=7.2505%

EAR for Bank 3=(1+0.1394%)^52-1=7.5126%

Periodic rate for Bank 4=RATE(16,-3281.53,45000)=1.8750%

Annual rate or APR for Bank 4=1.8750%*4=7.5000%

EAR for Bank 4=(1+1.8750%)^4-1=7.7136%

Lowest EAR is Bank 1 hence Michael should take loan from Bank 1