Question

You are considering to borrow Rs 100,000 from SBI for a period of one year and have the following options to choose from: Option A: SBI offering interest rate of 10% p.a. Option B: HDFC Bank is offering to give guarantee to SBI on your behalf subject to your paying a fee of 1% flat. Based on this guarantee, SBI is willing to reduce the interest rate to 9.5% p.a. Which option will you choose? Select one:

a. Option B

b. Option A

c. Both options are equally attractive

Answer 1

Option A:

Loan Amount = $ 100000

Interest rate = 10%

The Value of Loan after 1 year is given by FV of the loan:

FV= PV * (1+r)ⁿ

Here, PV is the present Value = 100000

r is the Interest rate = 10%

n is the number of periods =1

FV = 100000 * (1+0.1)¹

FV = 100000 * 1.1

FV = $ 110,000

Option B:

Loan amount = $ 100000

Fee = 1% * 100000 = 1000

Interest rate = 9.5%

Tenure = 1 year

FV of the loan is:

FV = PV * (1+r)ⁿ

Here, PV = Loan amount + Processing Fee = 100000 + 1000 = 101000 (Including the opportunity cost related to $ 1000 @ 9.5% p.a.)

r is the Interest rate = 9.5%

n is the Number of periods=1

FV = 101000 * (1+9.5%)¹

FV = 101000 * 1.095

FV = $ 110,595

In Option A, the value of the loan after 1 year is less than the value of the loan after 1 year in Option B. Hence, Option A should be chosen.