# Interest – Part II

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By : Varsha Deiveegan

This is Part 2 of “Interest”. Click here for Part I.

So, in SI the principal never changes i.e. it remains same for the entire period. But this is not how banks and insurance corporations calculate interest. Let us understand this with the help of illustrations.

Suppose you deposit Rs. 50000 in a bank for 2 years at 7% p.a. compounded annually. Interest will be calculated in the following manner-

Interest for the first year-

Using the SI formula,

I=PRT/100
= (50000*1*7)/ 100
= Rs.3500

Interest for the second year-

Principal for the second year would be the initial deposit plus interest for the first year. Therefore, the principal would be-

Rs.50000 + Rs.3500 = Rs.53500

Therefore interest is calculated as follows-

Rs.53500 * 1 * 7/100 = Rs.3745

Hence, total interest = Rs.3745 + Rs.3500 = Rs. 7245

So, compound interest can be defined as the interest that accrues when earnings for each specified period of time added to the principal thus increasing the principal base on which subsequent interest is computed. It is calculated as follows-

If P is the principal, i = rate of interest and n is the tenure/ period/ term, then the amount after n years is given by-

A = P (1+i)n

Therefore, Interest is calculated by = A – P = P (1+i)n – P = P [ ( 1 + i)n – 1]

Shortcuts

1.A sum of money will double itself in approximately 72/R years.
2.A sum of money will triple itself in 114/R years.
3.If a sum of money becomes n times in T years, then it will become nm times in m * T years.

But to use the above shortcuts, make sure that the interest rate is on per annum basis.

Note

1. When the interest is paid semi annually or half yearly then,
A = P (1 + i/2)2n

2. When interest is paid quarterly,
A = P (1 + i/4)4n

3. When interest is paid monthly,
A = P (1 + i/12)12n

Illustration 1: At what annual rate of interest, compounded yearly, will money double in 8 years?

72/ R = 8 (Rule of 72!)
R = 9%

Illustration 2: Approximately how long will it take to triple an investment at 10% Compounded annually?

(a)16.5 years
(b)15 years
(c)11.5 years
(d)15.5 years
114/10 = 11.4 (Rule of 114!)
The closest is 11.5 years

Illustration 3: A sum of money doubles itself in five years. In how many years will it become four fold if interest is compounded annually?

n = 2, T = 5, m = 2
using the formula(shortcut 3), T2 = m * T = 10

PRACTICE!! : There are 10 Questions below. Select an option and click “Next”. At the end, answers and explanations will be displayed.

1. The compound interest on a certain sum at 5% for 2 years is Rs.328. The SI for that sum at the same rate and for the same period will be?

2. If in two years a principal of Rs.100 amounts to Rs.121, when the rate of interest is compounded annually, then the value of r would be

3. In how many years will Rs.2000 amount to Rs.2420 at 10% per annum compounded annually?

4. If the difference between the compound interest, compounded every six months and simple interest on a sum of money at the rate of 12% per annum for one year is Rs.36, the sum is

5. The CI on a sum of money for two years is Rs.205 and the SI on the same sum for the same period at the same rate is Rs.200. Find the sum

6. A sum of money put at CI amounts to Rs.210 in 3 years and Rs.200 years. Find out the rate of interest.

7. The difference between CI and SI on a certain sum of one year at 5% per six months is Rs.3, then the sum is

8. The rate of interest at which an amount of Rs.1800 on CI becomes Rs.1984.50 in 2 years is

9. An amount of money grows up to Rs.8000 in 2 years and up to Rs.3500 in 3 years. Find the compounded rate of interest.

10. The population of a town is 20000. If the annual birth rate is 4% and annual death rate is 2%, the population after 2 years is

1. rachana

hey could you explain shortcut 3? cause when i apply it i dont get the right answer 🙂

2. Surbhi

Thanks for d exercise:-)
Cud u plz explain question 9…

3. Syamal Sengupta

Question nos. 6 and 9 seem to have incomplete information/
Thank you.