# Simple and Compound Interest

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Principal: The money borrowed out for a certain period is called the principal or the sum.

Interest: Some extra money paid for using other’s money is called interest.

Simple Interest (S.I.): When the sum borrowed for a certain period is computed uniformly, then it is called simple interest.

Compound Interest: The compound interest is interest calculated on the initial principal which also includes all of the accumulated interest of previous period of a deposit. The borrower and the lender agrees to fix up a certain unit of time, say yearly or half-yearly or quarterly to settle the previous account.

Formula for Simple Interest:

Let Principal = P, Rate = r% per annum, Time = T

Simple Interest = (Principal * Rate * Time / 100)

P = (100 * S.I. / Rate * Time); R = (100 * S.I. / Principal * Time); T = (100 * S.I. / Principal * Rate)

Formula for Compound Interest:

1. When interest is compound annually:

Amt = P (1 + R/100)n

1. When interest is compounded Half-yearly:

Amt = P [1 + (R/2)/100]2n

• When interest is compounded quarterly:

Amt = P [1 + (R/4)/100]4n

1. When interest is compounded annually but time is in fraction, like years

Amt = P (1 + R/100)3 * (1 + )

1. When rates are different for different years say R1%, R2%, Rx% for 1st, 2nd and 3rd year respectively.

Then, Amt = P (1 + R1/100) (1 + R2/100) (1 + R3/100)

1. Present worth of Rs. x due n years hence is given by:

Present Worth = x / (1 + R/100)n

Questions:

1. Shyam’s capital is 1/6 times more than Ram’s capital. Ram invested his capital at 20% per annum for 2 years (compounded annually). At what rate of percent p.a. simple interest should Shyam invest in his capital so that after 2 years, they both have the same amount of capital?

A)    10%

B)    11 5/7%

C)    20%

D)   13 5/7%

E)   None of these

Explanation:

Let the capital of Shyam= 6 and capital of Ram=7

6(1+20/100)3 = [7 + (7*R*2)] R = 11 5/7%

100

2. A certain sum of money amounts to Rs. 800 in 2 years and to Rs. 920 in 7/2 years. What will be the sum and the rate of interest?

A)   12%

B)   10%

C)   25%

D)   16%

E)   None of these

Explanation:

Simple Interest for 3/2 years = Rs. (920 – 800) = Rs. 120

So, Simple Interest for 2 year = Rs. (120 * 2/3 * 2) = Rs.160.

Principal = Rs. (800 – 160) = Rs.640

Now, P = 640, T = 2 and S.I. = 160

R = (100 * S.I. / P * T)

Rate of Interest = (100*160/640*2) = 25%.

3. If there is an increase of 60% in an amount in 6 years at simple interest than what will be the compound interest of Rs.14000 after 3 years at the same rate?

A)   4634

B)   2160

C)   6240

D)   3120

E)   None of these

Explanation:

Let P = Rs.100. Then, simple interest is Rs.60 and T = 6 years.

∴ R = 100*60/100*6 = 10% p.a.

Now,

P = Rs.14000 T = 3 years and R = 10% p.a.

∴ C.I. = Rs. [14000*{(1+10/100)3 -1}]

= Rs. (14000*331/1000)

= 4634

4. What will be the simple interest on Rs.3000 at 6 ¼ % p.a. for the period from 4 Feb 2019 to 18 April 2019?

A)    60

B)   38.40

C)   49.50

D)   37.50

E)   None of these

Explanation:

S.I = (P * R * T /100)

T = (24 + 31 + 18) days =73 days = 73/365 = 1/5 year.

P = Rs. 3000 and R = 6 ¼ % p.a. = 25/4 % p.a.

∴ S.I. = Rs. (3000 * 25/4 * 1/5 * 1/100) = Rs. 37.50

5. A woman borrows Rs.12000 at 20% compound interest. At the end of every year she pays Rs.2000 as part repayment. How much does she still needs to repay after three such installments?

A)    12000

B)   15600

C)   12864

D)   13250

E)   None of these