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**Answer:**

Let assume its equal after N years

Veeru’s investment after N years = 10000 + 10000 × (5/100) × N

Joy’s investment after N years = 8000 + 8000 × (10/100) × (N – 2)

Equating both

10000 + 10000 × (5/100) × N = 8000 + 8000 × (10/100) ×(N – 2)

10000 + 500N = 8000 + 800N – 1600

3600 = 300N

N = 12

**Answer:**

P (1.05) 2 – P = CI

P × 3 × 3/100 = SI

CI = 0.1025 P

SI = 0.09 P

CI – SI = 0.0125 P = 125/10000 P = 1125

P = 90000

**Answer:**

Total amount invested by Amal = 12000 (1+0.08) + 10000 (1 + 0.06/2) ^ 2 = 12960 + 10609 = 23569

Bimal invests p amount at SI

So, interest for bimal = p * 7.5 * 1/100

Interest are same for a and b, so we get

23569 – 22000 = p * 7.5 * 1/100

So, p = 20920

**Answer**:

Let each instalment be ₹x. Equating the present value of both the instalments to the money borrowed,

(x/1.1) + (x/1.12) = 210000

x = 121000

Interest is the amount charged from the borrower by the lender on the principal loan sum. Interest is the cost of renting money and the rate at which interest is charged on the principal sum which is known as the interest rate. The interest rate charged depends on two factors:

- The value of money does not remain the same over time. It changes with time. The net worth of ₹ 50 today will not be the same tomorrow i.e. If 5 pens could be bought presently with an INR 50 note then in the future, maybe only 4 pens can be bought with the same ₹ 50 note. The reason behind may be inflation or the hike in prices.
- The credibility of the borrower, if there is a chance of more risk and default on the borrower side then a high-interest rate is charged in the same way it will be lower if the risk factor is low and comparatively low default on the borrower side.

The above two reasons become the basis of why interest rates are so relevant and important at the same time have a great effect on markets and the economy and forms an integral & important part of the curriculum in the MBA or PGDM programs. But, a relatively simpler level of questions is asked in the CAT, XAT, NMAT and other management exams based on the concepts learned at the time of high school.

These concepts are categorized into a type of interests:

- Simple Interest
- Compound Interest

Let us first understand the concept of simple interest, It is a type of interest which once credited does not earn interest on itself and remains fixed over time.

The formula to calculate Simple Interest is**SI = {(P x R x T)/ 100}**

Where

P = Principal Sum (the deposited amount or original loan)

R = rate of interest (the rate at which loan is charged)

T = Time period (the duration for which money is borrowed or deposited)

So, If the amount of P is borrowed at the rate of interest R for the period of T years then the amount to be repaid to the lender will be given by**A = P + SI**

Suppose If rate to interest is r1% for T1 years, r2% for T2 years …. rn for Tn years for investment and the Simple Interest obtained is ₹x on the investment. Then the principal amount is given by

**x * 100 / (r1T1 + r2T2 + …+ rnTn)**

If a person deposits a sum of ₹X at r1% p.a. and the sum of ₹Y at r2% p.a. then the rate of interest for the sum deposited is given by

**R = {(Xr1 + Yr2) / (X + 1)}**

If a certain sum of money becomes “a” time in “T years” at Simple Interest, then the rate of interest p.a. is

**R = 100 (a – 1) / T**

Suppose a certain amount of money is lent out in n parts in such a way that an equal sum of money is available at simple interest on each part at the given interest rates at R1, R2, …, Rn respectively, and periods are mentioned as T1, T2, …, Tn respectively, then the ratio in which the sum that will be divided into n parts is given by

**1 / R1T1: 1 / R2T2….: 1 / RnTn**

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