Question

Emily borrowed a loan worth $1000, which she has to repay at the end of 5 years. The loan has a nominal interest rate of 4% (compounded twice a year) for the first 2 years, and a nominal interest rate of 6% (compounded 4 times a year) for the last 3 years.

i) Calculate the loan's original amount

ii) Calculate the EAR that was charged over the 5-year period

Answer 1

The loan has a nominal interest rate of 4% (compounded twice a year) for the first 2 years, and a nominal interest rate of 6% (compounded 4 times a year) for the last 3 years.

Effective rate of charging for semi-annually = 4%/2

= 2%

If you invest $1000 for four periods at 2 percent per period, the loan value is:

Loan amount = $1000 × 1.022

= $1,000 × 1.0404

= $1,040.40

Effective rate of charging for quarterly = 6%/4

= 1.5%

If you invest $1000 for four periods at 2 percent per period, the loan value is:

Loan amount = $1000 × 1.0154

= $1,000 × 1.00613

= $1,1040.18

Total interest charged = $40.4 + 104.18 = $144.58

Effective Annual Rate = interest charged / Borrowed amount

= $144.58 / $1,000

= 0.14458 or 14.46%

EAR = 14.46%

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