Mechanical Engineering Exam > Mechanical Engineering Notes > General Aptitude for GATE > Cheatsheet: Interest
Cheatsheet: Interest | General Aptitude for GATE - Mechanical Engineering PDF Download
Theory
Simple Interest is the interest earned when the borrower usually pays a fee to the lender each year and that fee is usually a percentage of amount borrowed at the start.
Compound Interest is the interest earned on the initial principal plus the interests earned over the previous periods of the loan.
Formula
- If a sum of money becomes x-times of itself in T-years @ R% p.a. S.I. then (x -1)100 = T×R
- If a sum of money becomes x1-times of itself in a time of T1-years @ R1% p.a.
S.I. it becomes x2-times of itself in T2-years @ R2% p.a. S.I. then
- A sum (P) of money becomes an amount of A1 in T1 years at a certain rate and the same sum becomes an amount of A2 in T2 years (T2 > T1). Then P = and the rate
- If the rates of compound interest are R1 , R2 , R3 ……….. Rn for n-successive years then
- If a sum of Rs P is lent out at R% p.a. compound interest for n-years then , if the interest is compounded half-yearly, if the interest is compounded quarterly
- The difference between compound interest and simple interest on a sum of Rs P for 2-years at R% p.a. is given by
Also, where S.I is simple interest for 2 years - The difference between compound interest and simple interest on a sum of Rs P for 3 years at R% p.a. is given by where S.I. is simple interest for 3-years
- If a sum of money amounts to An−1 and to An in (n – 1) and n years respectively then
and the rate 
, if the interest is compounded half-yearly
, if the interest is compounded quarterly
, where S.I is simple interest for 2 years
where S.I. is simple interest for 3-years
Solved Example
Question for Cheatsheet: InterestTry yourself:On a certain sum, the simple interest at the end of 5(1/3) years becomes 4/9 ofthe sum.What is the rate percent ?
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Question for Cheatsheet: InterestTry yourself:P is going to pay Rs.700 to Q, 7 months later at 6% annual simple interest, Q isgoing to pay Rs.550 to P, 12 months later at 8% annual simple interest, if theydecide to settle the debts, who will pay what amount to whom ?
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A father left a will of Rs.5 lakhs between his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.5 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?Question for Cheatsheet: InterestTry yourself: View Solution
The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?Question for Cheatsheet: InterestTry yourself: View Solution
Hari took an educational loan from a nationalized bank for his 2 years course of MBA. He took the loan of Rs.5 lakh such that he would be charged at 7% p.a. at CI during his course and at 9% CI after the completion of the course. He returned half of the amount which he had to be paid on the completion of his studies and remaining after 2 years. What is the total amount returned by Hari?Question for Cheatsheet: InterestTry yourself: View Solution
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FAQs on Cheatsheet: Interest - General Aptitude for GATE - Mechanical Engineering
| 1. What is interest banking? |  |
Ans. Interest banking refers to the practice of earning interest on deposits and providing loans or credit facilities to customers. Banks use the funds deposited by customers to lend money to borrowers, and in return, they pay interest to depositors based on the agreed-upon interest rate.
| 2. How does interest banking work? | |
Ans. Interest banking works by banks accepting deposits from customers and using those funds to provide loans and credit facilities to borrowers. Banks earn interest on the loans they provide, which is higher than the interest they pay to depositors. The difference between the interest earned and interest paid is the bank's profit.
| 3. What are the benefits of interest banking? | |
Ans. Interest banking offers several benefits. Firstly, it allows individuals and businesses to earn interest on their deposited funds, helping them grow their savings. Secondly, it provides access to credit facilities, allowing borrowers to finance their needs and projects. Lastly, interest banking plays a crucial role in the economy by facilitating the flow of funds between savers and borrowers.
| 4. How do banks determine interest rates in interest banking? | |
Ans. Banks determine interest rates in interest banking based on various factors. These factors include market conditions, the central bank's monetary policy, inflation rates, creditworthiness of borrowers, and the bank's own cost of funds. Banks aim to set interest rates that attract both depositors and borrowers while ensuring profitability.
| 5. What risks are associated with interest banking? | |
Ans. Interest banking involves certain risks. The main risks include credit risk, where borrowers may default on their loans, and interest rate risk, where changes in market interest rates can impact the profitability of banks. Banks also face liquidity risk if they are unable to meet deposit withdrawals or fund loan demands. Additionally, operational and regulatory risks are also present in interest banking.
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