AFB: Calculation of Interest

Calculation of Interest:

Banking business mainly consists of accepting deposits and lending. Bank pays interest to the depositors, on lending to customers; the bank charges a certain interest at a specified rate. The interest is payable either at periodic intervals or at the end of a loan period. Interest calculation can be Simple interest or compound interest.

Simple interest:

It is the amount of interest calculated as a fixed percentage of the amount borrowed or lent at the start and is paid or received at the end of the contracted period. In other words no interest is paid on the amount of interest

SI = Principal X Rate X Time

One question from this topic is asked directly every year for 0.5 or 1 mark.

Ques 1: A student purchases a computer by obtaining a loan on SI. The computer costs Rs. 1500 and the interest rate is 12% PA. If the loan is to be paid back after 2 years calculate

  1. The amount of total interest to be paid
  2. The total amount to be paid back after 2 years.

Sol: Interest to be paid I = PRT = 1500X12%X2 = 360

To calculate this in calculator type 1500X2X12%

Total amount to be paid back = Principal + Interest = 1500+360 = 1860.

Ques 2: Mr A has one savings account with the interest rate of 3.3%, and one money market account with the interest rate of 5.1%, in a bank. If he deposits Rs. 1200 to the savings account and Rs. 1800 to the money market account, how much money will he have after 6 years?

Sol: Savings account P = 1200

Interest earned after 6 years =  = 237.6

Total amount = 1200+237.6 = 1437.60

Money market account P=1800

Interest earned after 6 years =  = 550.8

Total amount = 1800+550.8 = 2350.80

Total amount = 1437.60+2350.80 = 3788.40

Try to use calculator to solve all the problems. Using calculator for higher powers and percentages must be handy.

Compound interest: When interest is paid by the borrower not on the amount of principal only but on the interest amount that has accrued also it is called compound interest.

Formula for calculation of amount due after a certain period on compound rate of interest is:  where

‘A’ is total amount due after n years,

‘P’ is the principal amount

‘R’ is rate of interest per annum expressed as fraction.

Compounding Rate R Years n
Annually R n
Half yearly R/2 2n
Quarterly R/4 4n
Monthly R/12 12n

Qus: Find the CI, if Rs 1000 was invested for 1.5 years at 20% p.a. compounded half yearly.

Sol: As it is said that the interest is compounded half yearly. So, the rate of interest will be halved and time will be doubled.

CI = P [1+(R/100)]n – P
CI = 1000 [1+(10/100)]3– 1000
On Solving, we get
CI = Rs. 331

Qus: The CI on a sum of Rs 625 in 2 years is Rs 51. Find the rate of interest.

Sol: We know that A = CI + P
A = 625 + 51 = 676
Now going by the formula: A = P [1+(R/100)]n
676 = 625 [1+(R/100)]2
676/625 = [1+(R/100)]2
We can see that 676 is the square of 26 and 625 is the square of 25
Therefore, (26/25)2 = [1+(R/100)]2
26/25 = [1+(R/100)]
26/25 – 1 = R/100
On solving, R = 4%

Ques: A sum of money is put on CI for 2 years at 20%. It would fetch Rs 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Sol: Let the Principal = Rs 100
When compounded annually,
A = 100 [1+20/100]2
When compounded half yearly,
A = 100[1+10/100]4
Difference, 146.41 – 144 = 2.41
If difference is 2.41, then Principal = Rs 100
If difference is 482, then Principal = 100/2.41 × 482
P = Rs 20000.

Amount becoming double of the amount lent:

On a compounded basis, when the amount is lent it becomes double after different time periods depending upon the rate of interest at which it has been borrowed. For this purpose the Rule of 72 can be used. According to this rule, to find out the time period during which the amount would become double, the number 72 is divided by the rate of interest.

For example, the money lent at 9% would become appx. double in 8 years(72/9) and the money lent at 8% would become appx double in 9 years(72/8).

FIXED AND FLOATING INTEREST RATES:

There are two different modes of interest. They are

  1. Fixed Rates &
  2. Floating Rates also called as variable rates.

Fixed Rate: In the fixed rate, the rate of interest is fixed. It will not change during entire period of the loan. The fixed rate is, normally, higher than floating rate, as it is not affected by market fluctuations.

Floating Rate: In the floating rate or variable rate, the rate of interest changes, depending upon the market conditions. Under floating rate, the interest rate is usually linked to a benchmark rate which could be the base rate of the bank or any other benchmark rate of the banking industry.

FRONT-END AND BACK-END INTEREST RATES

If the interest is deducted from the principal amount and only the net amount is disbursed, it is called front-end interest. For example when the bank discounts a bill, the interest applicable for the tenure of the bill is calculated and is deducted from the bill amount along with other charges and the net amount is paid to the customer.

The normal practice in banking industry is to charge back-end interest rate which means that the full amount of the loan is disbursed and the interest is charged subsequently on monthly/quarterly/agreed basis.


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