Simple Interest & Compound Interest

The interest is payable on the principal is known as Simple Interest.

Formula for simple interest ( S.I) is : = (P x R x T)/100 Where, P = principal or sum being borrowed. R = Rate of interest per year. T = Time for which the sum is borrowed. Amount = Principal + S.I. If T is not a whole number, then the period is

represented as a fraction of a yea, i.e. 1month = 1/12 year.

The principal grows at a constant rate in absolute terms.

Simple Interest

In Compound Interest, the amount received at the end of 1st year becomes principal for 2nd year, and so on. The principal grows at an increasing rate in absolute terms. The interest is calculated on the new principal at the end of every time period.

Formula for Compound Interest; C.I = P (1+(r/100))ⁿ-P Where P = Principal, r = rate of interest,

n=time period. Amount = P (1+(r/100))ⁿ

Compound Interest

Compounding done per Year

Interest added to Principal every

year

Annually 1 1 year

Semi - Annually 2 6 months

Quarterly 4 3months

Monthly 12 1 month

Non – Annual Compounding

When C.I. is compounded annually C.I = P (1+(r/100))ⁿ-P Semi – Annually; C.I = P (1+((r/2)/100))²ⁿ-P Quarterly ; C.I = P (1+((r/4)/100))⁴ⁿ-P Monthly ; C.I = P (1+((r/12)/100))¹²ⁿ-P

NOTE:I. If the word interest is given and nothing else is specified, the

interest is considered as S.I.II. If the interest is given by bank and nothing is specified, it is

always C.I.III. Population growth is always taken as compounding basis.IV. The difference between C.I & S.I for 2 years is given by

P(R/100)²

Type 1# Given interest amount for n years at rate r

%. What is the principal.

Example: A certain amount earns a simple interest of Rs 250 in 4 years at 5% p.a. What is the amount?

Types of Questions

Type 2# A amount becomes X times in n years at

compound interest. What is the rate per annum?

Example: A amount becomes 2 times in 2 years at C.I. What is the rate of Interest?

Type 3# Which would lead to a higher amount:a. r₁% simple interest for t₁ time.b. r₂ % simple interest for t₂ time.

Example: Mr. Sharma wants to chose a investment plan:

1. 15% for 5 years. (S.I.)2. 20% for 3 years. (C.I.) Which plan will result in higher amount?

Type 4# The C.I in the nth year is Rs. X and C.I in

nth+ 1 year is Rs. Y. What is the rate of interest.

A certain sum of money in 7th year is Rs 600 and the same amount in 8th year is Rs 660. What is the rate of interest?

Type 5# The total S.I in first two years is Rs. X and

total C.I in first two years is Rs. Y. What is the rate of interest and principal, if they are same for S.I and C.I?

Example: Total S.I in First 2 years is Rs. 600.

If the same amount was kept at C.I at same rate, total C.I would be Rs.660 . What is the principal and rate of interest?

Type 6# A principal amounts to X times in T years at

S.I. In how many years will it become Y times?

Example: Amount becomes 3 times in 5 years. In how many years will it become 9 times? Assume S.I

Type 7# A principal amounts to X times in T years at

C.I. In how many years will it become Y times?

Example: Amount becomes 3 times in 5 years. In how many years will it become 9 times? Assume C.I