Homework Answers
Loan amount = $ 40000
Annual rate of interest = 3.9%
monthly interest rate = 0.325%
Frequency of compounding in a year = monthly or 12
term of loan = 10 years
no. of payment period per year = 10*12 = 120 months
Monthly Installment amount = Loan Amount/PVIFA(0.325%,120months)
=40000/99.23533
= 403.08
Total interest paid = $ 8369.87 in 10 years.
Effective rate of interest = (1+nominal rate of interest/no. of compounding in a year)^(no. of payment period per year) - 1
= (1+0.039/12)^(12) - 1
= (1+0.00325)^(12) - 1
= 1.00325^(12) - 1
= 1.0397 - 1
= 0.0397 or 3.97%
or 3.9704732701%
When compounding/discounting has to be done at intervals less than a year, a distinction should be made between (i) nominal and (ii) effective rate of interest. The coupon rate of interest is called the nominal rate of interest. The nominal rate of interest differs from the effective rate of interest due to the frequency of compounding (e.g annual, halfyearlt, quaterly, monthly) with the nominal rate. with annual compounding/conversion, the nominal rate and the effective rate would be the same. The effective rate of interest is higher and inceases with an increase in the frequency of compounding.
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