Question

Compute the nominal annual rate of interest compounded semi annually on a loan of $48,000 repiad in installements of $4,000 at the end of every sixc months for ten years Round answer to 2 decimal places.

Answer 1

Loan amount = 48000

Repayment at every 6 months = 4000

Total number of payments to be made = 10*2 = 20

Present value of total repayment = 4000*Present value annuity factor(r, 20)

Present value of loan amount = 48000

As per Internal rate of return equation:

Present value of loan amount = Present value of total repayment

48000 = 4000*Present value annuity factor(r, 20)

48000/4000 = Present value annuity factor(r, 20)

12 = Present value annuity factor(r, 20)

Now we have to find the value of r whose annuity value for 20 periods is equal to 12.

Let r = 5%

Present value annuity factor (5%, 20) = 12.46

Let r = 6%

Present value annuity factor (6%, 20) = 11.47

By interpolation method:

IRR = 5% + [(12.46 – 12)/(12.46 – 11.47)]/(6% - 5%)

= 5% + (0.46/0.99) *1%

= 5% + 0.46% = 5.46%

Nominal annual rate of interest compounded semi annually = 5.46%*2 = 10.92%