# bank loan interest rates

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```					Interest Calculation Primers: IIMB Microfinance Group

1. Simple Interest
You deposit Rs 1,000 with a bank, that offers to pay 10% simple interest per annum.
What will be the total amount you will receive if you deposit the amount for (a) 1
Year (b) 2 Years (c) 3 Years (d) 10 Years (e) 25 Years. In addition to the total amount
received show the principal and interest separately.
Hint

Step 1 Write down the principal amount (the amount initially deposited)

Step 2 Calculate the interest amount
Interest (Amount)=Principal*Interest Rate*Period
[If the interest rate is annual, as in this example, the period should be in years to
ensure consistency]

Step 3 Total = Principal + Interest

(a) 1 Year
Principal
Interest
Total

(b) 2 Years
Principal
Interest
Total

(c) 3 Years
Principal
Interest
Total

(d) 10 Years
Principal
Interest
Total

(e) 25 Years
Principal
Interest
Total

January 2007                                                                            1
Interest Calculation Primers: IIMB Microfinance Group

2. Compound Interest
You deposit Rs 1,000 with a bank that offers to pay a 10% per annum compounded
annually. What will be the total amount you will receive if you deposit the amount for
(a) 1 Year (b) 2 Years (c) 3 Years (d) 10 Years (e) 25 Years. In addition to the total
amount received show the principal and interest separately.
Hint

Step 1 Write down the principal amount (the amount initially deposited)

Step 2 Calculate the total amount
Total=Principal*(1+Interest Rate)Period

Step 3 Interest (Amount) =Total- Principal

(a) 1 Year
Principal
Interest
Total
Hint
Total=Principal*(1+Interest Rate)

(b) 2 Years
Principal
Interest
Total
Hint
Total=Principal*(1+Interest Rate)2
= Principal*(1+Interest Rate)*(1+Interest Rate)

(c) 3 Years
Principal
Interest
Total
Hint
Total = Principal*(1+Interest Rate)3
= Principal*(1+Interest Rate)*(1+Interest Rate)*(1+Interest Rate)

(d) 10 Years
Principal
Interest
Total

(e) 25 Years
Principal
Interest
Total

January 2007                                                                           2
Interest Calculation Primers: IIMB Microfinance Group

3. Effective Interest Rates
A bank offers you a loan with a stated annual interest rate of 10% per annum. What is
the effective annual interest rate with (a) Annual rest (b) Semi-annual rests (c)
Quarterly rests (d) Monthly rests. Semi-annual rests mean that interest will be applied
at 5% (10%/2) every six months, the compounding period being six months. Quarterly
rests mean that interest will be applied at 2.5% (10%/4) every three months, the
compounding period being three months.

Hint
Effective Annual Interest Rate
=(1+Stated Annual Interest Rate/No. of Intervals)No. of Intervals - 1

For example with semi-annual compounding the number of intervals in a year is 2.

Compounding                No. of months         No. of Intervals      Effective   Interest
Period                                                                 Rate
Annual                     12                    1

Semi-annual                6                     2

Quarterly

Monthly                    1

January 2007                                                                                  3
Interest Calculation Primers: IIMB Microfinance Group

4.1 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on a declining balance basis. What
is the effective annual interest rate?

4.2 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on a declining balance basis. An
up-front application fee of 2% of the loan principal is charged. What is the effective
annual interest rate?

4.3 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on a declining balance basis. An
amount equal to 10% of the loan principal will have to be compulsorily saved at zero
percent interest rate. This amount can be withdrawn after the loan has been fully repaid.
What is the effective annual interest rate?

4.4 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on a declining balance basis. An
up-front application fee of 2% of the loan principal is charged. An amount equal to 10%
of the loan principal will have to be compulsorily saved at zero percent interest rate. This
amount can be withdrawn after the loan has been fully repaid. What is the effective
annual interest rate?

5.1 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on flat basis. What is the effective
annual interest rate?

5.2 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on a flat basis. An up-front
application fee of 2% of the loan principal is charged. What is the effective annual
interest rate?

5.3 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on flat basis. An amount equal to
10% of the loan principal will have to be compulsorily saved at zero percent interest rate.
This amount can be withdrawn after the loan has been fully repaid. What is the effective
annual interest rate?

5.4 A bank gives a loan of Rs 1,200 to be repaid in twelve monthly instalments. Interest will
be charged monthly at a stated rate of 24% per annum on flat basis. An up-front
application fee of 2% of the loan principal is charged. An amount equal to 10% of the
loan principal will have to be compulsorily saved at zero percent interest rate. This
amount can be withdrawn after the loan has been fully repaid. What is the effective
annual interest rate?

January 2007                                                                              4
Interest Calculation Primers: IIMB Microfinance Group

6   An MFI has opening loan portfolio of 1,000. It charges a stated rate of interest of 24% per
annum.

6.1 Suppose the MFI charges an interest rate payable annually, and the portfolio can only
grow out of reinvested interest earnings what is the Effective Interest Rate (on an annual
compounding basis? Compute the yield on the average loan portfolio. What is the
Yield/APR ratio and the return on the initial portfolio?

6.2 Suppose the MFI applies the stated interest rate on a monthly basis and re-invests interest
earned in the loan portfolio.      What is the Effective Interest Rate (on an annual
compounding basis? Compute the yield on the average loan portfolio. What is the
Yield/APR ratio and the return on the initial portfolio?

7. A bank gives a loan of Rs 1,040 to be repaid in 52 weekly instalments, with repayment
commencing the week following the disbursement. Interest will be charged weekly at a
stated rate of 24% per annum on flat basis. What is the effective annual interest rate?

January 2007                                                                             5

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