Let Principal = P, Rate = R% per annum, Time = n years.
When interest is compound Annually:
Amount = P
1 +
R
n
100
When interest is compounded Half-yearly:
Amount = P
1 +
(R/2)
2n
100
When interest is compounded Quarterly:
Amount = P
1 +
(R/4)
4n
100
When interest is compounded Annually but time is in fraction, say 3 years.
Amount = P
1 +
R
3
x
1 +
R
100
100
When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.
Then, Amount = P
1 +
R1
1 +
R2
1 +
R3
.
100
100
100
Present worth of Rs. x due n years hence is given by:
Present Worth =
x
.
1 +
R
100
Questions:
Level-I:
1.
A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
The difference between simple and compound interests compounded annually on a certain sum of Money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R =
100 x 60
= 10% p.a.
100 x 6
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I.
= Rs.
12000 x
1 +
10
3
– 1
100
= Rs.
12000 x
331
1000
= 3972.
Answer:4 Option A
Explanation:
C.I. when interest compounded yearly
= Rs.
5000 x
1 +
4
x
1 +
x 4
100
100
= Rs.
5000 x
26
x
51
25
50
= Rs. 5304.
C.I. when interest is compounded half-yearly
= Rs.
5000 x
1 +
2
3
100
= Rs.
5000 x
51
x
51
x
51
50
50
50
= Rs. 5306.04
Difference = Rs. (5306.04 – 5304) = Rs. 2.04
Answer:5 Option A
Explanation:
Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000
1 +
7
n
= 34347
100
107
n
=
34347
=
11449
=
107
2
100
30000
10000
100
n = 2 years.
Answer:6 Option C
Explanation:
Amount
= Rs.
25000 x
1 +
12
3
100
= Rs.
25000 x
28
x
28
x
28
25
25
25
= Rs. 35123.20
C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20
Answer:7 Option A
Explanation:
Let the rate be R% p.a.
Then, 1200 x
1 +
R
2
= 1348.32
100
1 +
R
2
=
134832
=
11236
100
120000
10000
1 +
R
2
=
106
2
100
100
1 +
R
=
106
100
100
R = 6%
Answer:8 Option B
Explanation:
P
1 +
20
n
> 2P
6
n
> 2.
100
5
Now,
6
x
6
x
6
x
6
> 2.
5
5
5
5
So, n = 4 years.
Answer:9 Option C
Explanation:
Amount
= Rs.
8000 x
1 +
5
2
100
= Rs.
8000 x
21
x
21
20
20
= Rs. 8820.
Answer:10 Option D
Explanation:
Amount of Rs. 100 for 1 year when compounded half-yearly
= Rs.
100 x
1 +
3
2
= Rs. 106.09
100
Effective rate = (106.09 – 100)% = 6.09%
Answer:11 Option C
Explanation:
C.I.
= Rs.
4000 x
1 +
10
2
– 4000
100
= Rs.
4000 x
11
x
11
– 4000
10
10
= Rs. 840.
Sum = Rs.
420 x 100
= Rs. 1750.
3 x 8
Answer:12 Option A
Explanation:
Sum = Rs.
50 x 100
= Rs. 500.
2 x 5
Amount
= Rs.
500 x
1 +
5
2
100
= Rs.
500 x
21
x
21
20
20
= Rs. 551.25
C.I. = Rs. (551.25 – 500) = Rs. 51.25
Answer:13 Option B
Explanation:
S.I. = Rs
1200 x 10 x 1
= Rs. 120.
100
C.I. = Rs.
1200 x
1 +
5
2
– 1200
= Rs. 123.
100
Difference = Rs. (123 – 120) = Rs. 3.
Answer:14 Option A
Explanation:
15000 x
1 +
R
2
– 15000
–
15000 x R x 2
= 96
100
100
15000
1 +
R
2
– 1 –
2R
= 96
100
100
15000
(100 + R)2 – 10000 – (200 x R)
= 96
10000
R2 =
96 x 2
= 64
3
R = 8.
Rate = 8%.
Answer:15 Option B
Explanation:
Let the sum be Rs. P.
Then,
P
1 +
10
2
– P
= 525
100
P
11
2
– 1
= 525
10
P =
525 x 100
= 2500.
21
Sum = Rs . 2500.
So, S.I. = Rs.
2500 x 5 x 4
= Rs. 500
100
Answer:16 Option D
Explanation:
Let Principal = Rs. P and Rate = R% p.a. Then,
Amount = Rs.
P
1 +
R
4
100
C.I. =
P
1 +
R
4
– 1
100
P
1 +
R
4
– 1
= 1491.
100
Clearly, it does not give the answer.
Correct answer is (D).
Answer:17 Option C
Explanation:
I. Amount = Rs.
200 x
1 +
6
16
100
II. Amount = Rs.
200 x
1 +
6
16
100
Thus, I as well as II gives the answer.
Correct answer is (C).
Answer:18 Option E
Explanation:
Given: T = 3 years.
I. gives: R = 8% p.a.
II. gives: S.I. = Rs. 1200.
Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained.
So, the correct answer is (E).
,
Compound interest is the interest you earn on your interest. It’s one of the most important concepts in personal finance, and it can have a big impact on your financial future.
Simple interest is the interest you earn on the principal amount of your Investment. For example, if you invest $100 at 5% simple interest, you’ll earn $5 in interest after one year.
Compound interest is different because you earn interest on both the principal amount and the interest you’ve already earned. This means that your interest earnings grow over time, and your investment can grow much faster than with simple interest.
To calculate compound interest, you use the following formula:
$A = P(1 + r/n)^nt$
Where:
$A$ is the future value of your investment
$P$ is the principal amount
$r$ is the interest rate
$n$ is the number of compounding periods per year
$t$ is the number of years
For example, let’s say you invest $100 at 5% interest, compounded annually. After one year, your investment will be worth $105. After two years, it will be worth $110.25. And after three years, it will be worth $115.76.
As you can see, the longer you invest your money, the more compound interest you’ll earn. And the higher the interest rate, the more your investment will grow.
There are a few things to keep in mind when it comes to compound interest:
The sooner you start investing, the more time your money has to grow.
The higher the interest rate, the more your money will grow.
The more often your interest is compounded, the more your money will grow.
If you’re serious about building wealth, it’s important to understand compound interest and how it can work for you. By taking advantage of compound interest, you can grow your money much faster than you would with simple interest.
Here are a few tips for using compound interest to your advantage:
Start investing early. The sooner you start investing, the more time your money has to grow.
Invest regularly. Even if you can only invest a small amount each month, it will add up over time.
Invest in high-interest-rate accounts. The higher the interest rate, the more your money will grow.
Choose investments that compound interest frequently. The more often your interest is compounded, the more your money will grow.
By following these tips, you can use compound interest to build wealth and reach your financial goals.
In addition to compound interest, there are a few other financial concepts that are important to understand. These include:
Simple interest: Simple interest is the interest you earn on the principal amount of your investment.
Effective annual rate (EAR): The EAR is the actual interest rate you earn on an investment, taking into account compounding.
Annual Percentage yield (APY): The APY is the annual rate of return on an investment, including compounding.
Compounding periods: The number of times per year your interest is compounded.
Continuous compounding: Continuous compounding is when your interest is compounded every instant.
Future value of an annuity: The future value of an annuity is the total amount of money you’ll have at the end of a period of time, given a certain interest rate and payment amount.
Present value of an annuity: The present value of an annuity is the amount of money you’d need to invest today to have a certain amount of money in the future, given a certain interest rate and payment amount.
Amortization: Amortization is the process of paying off a loan over time.
Loan repayment: Loan repayment is the process of paying back a loan.
Depreciation: Depreciation is the decrease in the value of an asset over time.
Inflation: Inflation is the increase in the general level of prices over time.
Investing: Investing is the process of putting money into something with the expectation of making a profit.
Retirement planning: Retirement planning is the process of saving and investing money for retirement.
Financial planning: Financial planning is the process of managing your money to achieve your financial goals.
By understanding these financial concepts, you can make informed decisions about your money and reach your financial goals.
What is the difference between simple interest and compound interest?
Simple interest is calculated on the principal amount only, while compound interest is calculated on the principal amount plus any interest that has already accrued. This means that compound interest can grow much faster than simple interest.
What is the formula for compound interest?
The formula for compound interest is A = P(1 + r/n)^nt, where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
What is the rule of 72?
The rule of 72 is a shortcut for estimating how long it will take for an investment to double at a given interest rate. To use the rule of 72, divide 72 by the interest rate. For example, if the interest rate is 8%, it will take about 9 years for the investment to double.
What is the difference between annual percentage rate (APR) and effective annual rate (EAR)?
The APR is the interest rate that is advertised by a lender. The EAR is the actual interest rate that you will pay, taking into account compounding. The EAR is always higher than the APR.
What is a sinking fund?
A sinking fund is a Savings account that is used to pay off a debt. The money in the sinking fund is invested in safe investments, such as Bonds or CDs. When the debt comes due, the money in the sinking fund is used to pay off the debt.
What is a balloon payment?
A balloon payment is a large payment that is due at the end of a loan term. Balloon payments are often used in mortgages and car loans.
What is a prepayment penalty?
A prepayment penalty is a fee that is charged if you pay off a loan early. Prepayment penalties are often used in mortgages and car loans.
What is a secured loan?
A secured loan is a loan that is backed by collateral. The collateral is something of value that you own, such as a car or a house. If you do not repay the loan, the lender can take the collateral.
What is an unsecured loan?
An unsecured loan is a loan that is not backed by collateral. Unsecured loans are often more risky for lenders, so they tend to have higher interest rates.
What is a credit score?
A credit score is a number that lenders use to assess your creditworthiness. Your credit score is based on your credit history, which includes your payment history, the amount of debt you owe, and the length of your credit history.
What is a credit report?
A credit report is a document that contains information about your credit history. Your credit report includes your credit score, your payment history, the amount of debt you owe, and the length of your credit history.
What is a debt consolidation loan?
A debt consolidation loan is a loan that is used to pay off multiple debts. Debt consolidation loans can help you to save money on interest and to simplify your monthly payments.
What is a debt settlement?
Debt settlement is a process in which you negotiate with your creditors to lower the amount of debt you owe. Debt settlement can be a risky option, and it is important to understand the risks before you decide to pursue it.
What is bankruptcy?
Bankruptcy is a legal process that allows you to discharge your debts. Bankruptcy can be a last resort, and it is important to understand the consequences of bankruptcy before you decide to file for it.
What is the formula for compound interest?
A. $A = P(1 + r/n)^nt$
B. $A = P(1 + r)^n$
C. $A = P(1 + r/n)^n$
D. $A = P(1 + r)^nt$
What is the difference between simple interest and compound interest?
A. Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount plus interest earned.
B. Simple interest is calculated annually, while compound interest can be calculated more frequently.
C. Simple interest is a more accurate way to calculate interest, while compound interest is an approximation.
D. Simple interest is a more common way to calculate interest, while compound interest is less common.
What is the effect of compounding interest more frequently?
A. It increases the amount of interest earned.
B. It decreases the amount of interest earned.
C. It has no effect on the amount of interest earned.
D. It can either increase or decrease the amount of interest earned, depending on the interest rate and the number of compounding periods.
What is the rule of 72?
A. The rule of 72 is a way to estimate how long it will take for an investment to double at a given interest rate.
B. The rule of 72 is a way to estimate how much interest an investment will earn at a given interest rate.
C. The rule of 72 is a way to estimate how much an investment will be worth at a given interest rate.
D. The rule of 72 is a way to estimate the annual percentage yield (APY) of an investment.
What is the difference between annual percentage rate (APR) and effective annual rate (EAR)?
A. APR is the interest rate that is advertised, while EAR is the actual interest rate that is paid.
B. APR is the interest rate that is paid on the principal amount, while EAR is the interest rate that is paid on the principal amount plus interest earned.
C. APR is calculated annually, while EAR is calculated more frequently.
D. APR is a more accurate way to calculate interest, while EAR is an approximation.
What is the difference between simple interest and amortized interest?
A. Simple interest is calculated on the principal amount, while amortized interest is calculated on the principal amount plus interest earned.
B. Simple interest is paid in full at the end of the loan term, while amortized interest is paid over the life of the loan.
C. Simple interest is a more common way to calculate interest, while amortized interest is less common.
D. Simple interest is a more accurate way to calculate interest, while amortized interest is an approximation.
What is the difference between a fixed-rate loan and an adjustable-rate loan?
A. A fixed-rate loan has a constant interest rate for the life of the loan, while an adjustable-rate loan has an interest rate that can change over time.
B. A fixed-rate loan is more common for mortgages, while an adjustable-rate loan is more common for car loans.
C. A fixed-rate loan is a more accurate way to calculate interest, while an adjustable-rate loan is an approximation.
D. A fixed-rate loan is a more risky loan, while an adjustable-rate loan is a less risky loan.
What is the difference between a balloon payment loan and an installment loan?
A. A balloon payment loan has a large payment due at the end of the loan term, while an installment loan has equal payments made over the life of the loan.
B. A balloon payment loan is more common for mortgages, while an installment loan is more common for car loans.
C. A balloon payment loan is a more accurate way to calculate interest, while an installment loan is an approximation.
D. A balloon payment loan is a more risky loan, while an installment loan is a less risky loan.
What is the difference between a secured loan and an unsecured loan?
A. A secured loan is backed by collateral, while an unsecured loan is not backed by collateral.
B. A secured loan is more common for mortgages, while an unsecured loan is more common for car loans.
C. A secured loan is a more accurate way to calculate interest, while an unsecured loan is an approximation.
D. A secured loan is a more risky loan, while an unsecured loan is a less risky loan.
What is the difference between a prime rate loan and a subprime rate loan?
A. A prime rate loan is a loan with an interest rate that is based on the prime rate
years.
R
years at 4% per annum compounded yearly and half-yearly?
R =
C.I.
x 4
Difference = Rs. (5306.04 – 5304) = Rs. 2.04
n = 2 years.
C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20
1 +
R = 6%
Effective rate = (106.09 – 100)% = 6.09%
Sum = Rs.
Difference = Rs. (123 – 120) = Rs. 3.
15000
15000
R
R = 8.
Rate = 8%.
P =
Sum = Rs . 2500.
C.I. =
Correct answer is (D).
Correct answer is (C).
Difference between C.I. and S.I. may be obtained.