Under normal circumstances, interest is always levied according to the actual loan balance, so there is no need to convert interest rates. Other expenses or expense rates need to be converted into actual annual rates, because the total loan amount may be gradually withdrawn and repaid. Other expenses can be divided into one-time payment and annual payment.
Actual annual interest rate of one-time expenses = one-time expenses ÷ (total loan amount × actual loan term)
The annual interest rate of the actual expenses paid each year = (annual expenses paid × loan term) ÷ (total loan amount × actual loan term)
Actual interest rate = actual annual interest rate of one-time expenses+actual annual interest rate of expenses paid every year+interest rate.
Example: known loan/kloc-USD 0/billion, with annual interest rate of 65,438+00% for 7 years. According to the agreement, the grace period is 3 years, the repayment period is 4 years, and the principal is repaid in four equal installments. The borrower makes a one-time withdrawal immediately after signing the contract, without paying the commitment fee. He needs to pay a one-time management fee of 0.5% of the loan amount, and he also needs to pay other expenses of $50,000 every year. Find the effective interest rate.
Solution: In this case, the actual loan term is 5.5 years.
(0.5%× 1 billion) /( 1 billion× 5.5) ≈ 0.095438+0%
The actual annual rate of one-time payment of management fee is 0.09 1%.
(50,000× 7)/(1billion× 5.5) ≈ 0.064%
The actual annual expense rate of other expenses is 0.064%.
0.09 1%+0.064%+ 10%= 10. 155%
The effective interest rate is 10. 155%. Considering the time value of money, the following formula is used to calculate the real interest rate:
Where l is the present value of the loan amount, m is the one-time payment fee, n is the number of interest payments, C 1, C2 and C3. It is the amount of repayment of principal and interest and other expenses for the first time, the second time and the nth time respectively, and R is the effective interest rate.
Example: The known conditions are the same as those in the previous example, and the actual interest rate obtained by accurate calculation method is found.
Solution: L= 1 billion dollars.
M=0.5%× 1 billion = USD 05 million.
C 1 = C2 = C3= 1 billion×10%+50,000 = 10.05 million USD.
C4 = 2500 million+10/000×10%+50,000 = USD 35.05 million.
C5 = 25 250,000+75 million×10%+50,000 = 32.55 million USD.
C6 = 2500 million+500 million×10%+50,000 = USD 30.05 million.
C7 = 2500 million+25 million×10%+50,000 = 27.55 million USD.
Substitute these data into the accurate calculation formula of the real interest rate:
The marking unit is (ten thousand)
r= 10. 19%
According to the accurate calculation method, the real interest rate is 10. 19%. It not only reflects other expenses in the loan, but also reflects the time value of money. Strictly speaking, only the effective interest rate can truly reflect the total cost of loans.