Question

You wish to borrow $2,000 for 2 years to start a business. You approach different lenders who have the following offers. Which is the best lender to borrow from? All percentage rates are rounded to 6 decimal places.

Select one: a. 11.345227% pa APR compounding weekly where there are exactly 52 weeks per year.

b. 10.934509% pa APR compounding semi-annually where there are exactly 2 semi-annual periods per year.

c. 0.218177% as an effective weekly rate where there are exactly 52 weeks per year.

d. 2.873734% as an effective quarterly rate where there are exactly 4 quarters per year.

e. I'll lend you the $2,000 now if you pay me a single payment of $2,508.8 in 2 years, with no other payments in between

Answer #1

we need to calculate effective annual rate and then we choose lendor whoose effective rate is lower

effective rate = (1+per period rate )^no of compounding periods

**A) 11.345227 compounding weekly**

effective rate is (1+0.11345227/52)^52 - 1 = 12%

**B) 10.934509% pa (semi annual compounding )**

effective rate = (1+ 0.10934509/2)^2 -1 **=11.23%**

**C)0.218177% weekly rate**

effective annual rate = (1+0.00218177)^52 -1 **=
11.99%**

**D)2.873734% quarterrly rate**

effevtive annual rate = (1+0.02873734)^4 -1 = 11.99%

**E) to pay 2508.8 in 2 years for 2000 today**

interest% = (2508.8 -2000)/2000 = 25.44%(for 2 years )

effective annual rate = (1.2544)^1/2 -1 **= 12%**

**conclusion** **out
of the above option b has lowest effective rate**

**so option B lender is best**

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