Question

Simple and compound interest rate

8. Determine the effective interest rate, based on a 15% annual rate with monthly capitalization:

a) effective monthly rate,

b) effective quarterly rate,

c) semi-annual effective rate,

d) annual rate effective.

9. Determine the effective annual interest rate, based on the nominal interest rate that is provided:

a) 9% per year with capitalization annually,

b) 6.8% per year with capitalization semi-annually,

c) 11% per year with capitalization monthly.

10. Determine the semi-annual effective interest rate, based on the nominal interest rate provided:

a) 11.3 per annum with monthly capitalization

b) 5% per annum with quarterly capitalization,

c) 7% per annum with semiannual capitalization,

Answer 1

8.

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = (1 + Rate/ Compounding period) Compounding period – 1

         = (1 + 0.15/12)12 – 1

         = (1 + 0.0125)12 – 1

         = 1.1607545 – 1

         = 16.07545%

Hence, the EAR is 16.07545%.

a.

Compute the effective monthly rate, using the equation as shown below:

Effective monthly rate = Effective annual rate/ 12

                                     = 16.07545%/ 12

                                     = 1.3396208%

Hence, the effective monthly rate is 1.3396208%.

b.

Compute the effective quarterly rate, using the equation as shown below:

Effective quarterly rate = Effective monthly rate*3 months

                                      = 1.3396208%*3 months

                                      = 4.0188624%

Hence, the effective quarterly rate is 4.0188624%.

c.

Compute the semi-annual effective rate, using the equation as shown below:

Semi-annual rate = Effective monthly rate*6 months   

                            = 1.3396208%*6 months

                            = 8.0377248%

Hence, the semi-annual rate is 8.0377248%.

d.

Compute the effective annual rate (EAR), using the equation as shown below:

EAR = (1 + Rate/ Compounding period) Compounding period – 1

         = (1 + 0.15/12)12 – 1

         = (1 + 0.0125)12 – 1

         = 1.1607545 – 1

         = 16.07545%

Hence, the EAR is 16.07545%.