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Here we provide you with Applied Maths Chapter 14, to help you gain a comprehensive understanding of the chapter and its concepts.
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Applied Maths Chapter 14 Solutions
Compound Interest And Annuity
EXERCISE – 14.1
Q.1 Find the amount and the compound interest on Rs.8000 at 5% per annum for 2 years.
Ans. Principal = Rs.8000 , r = 5% , T = 2 years
Interest on 1st year= (P x R x T)/100
= (8000 x 5 x 1)/100
= Rs.400
Principal for 2nd year = 8000 + 400
= Rs.8400
Interest on 2nd year=(PxRxT)/100
= (8400 x 5 x 1)/100
= Rs. 420
Total Interest = 400 + 420 = Rs.820
Total Amount = 8000 + 820 = Rs.8820
Q.2 A man invests Rs.46875 at 4% per annum compound interest for 3 years. Calculate:
(i) the interest for the first year.
(ii) the amount standing to his credit at the end of the second year.
(iii) the interest for the third year.
Ans.
(i) Interest for 1st year = (PxRxT)/100
= (46875 x 4 x 1)/100
= Rs.1875
(ii) Principal for 2nd year =
46875 + 1875
= Rs.48750
Interest for 2nd year =
(PxRxT)/100
= (48750 x 4 x 1)/100
= Rs. 1950
Amount at the end of 2nd year = 46875 + 1875 + 1950
= Rs.50700
(iii) Principal for 3rd year = Rs.50700
Interest for 3rd year = (PxRxT)/100
= (50700 x 4 x 1)/100
= Rs. 2028
Q.3 A man invests Rs.5000 for three years at a certain rate of interest, compounded annually. At the end of one year, it amounts to Rs.5600. Calculate:
(i) the rate of interest per annum.
(ii) the interest accrued in the second year.
(iii) the amount at the end of the third year.
Ans.
(i) Principal = Rs.5000 , r = ? , A = Rs.5600
Interest for 1st year = 5600 – 5000
= Rs. 600
Therefore,
Interest = (P x R x T)/100
600 = (5000 x R x 1)/100
R = 12%
(ii) Principal for 2nd year = Rs.5600
Interest on 2nd year = (PxRxT)/100
= (5600 x 12 x 1)/100
= Rs. 672
(iii) Principal for 3rd year =
5600 + 672
= Rs.6272
Interest for 3rd year = (PxRxT)/100
= (6272 x 12 x 1)/100
= Rs. 752.64
Amount = 6272 + 752.64
= Rs.7024.64
Q.4 Find the amount and the compound interest on Rs.2560 for 1 1/2 years at 6 1/4% per annum the, interest being compounded semi-annually.
Ans. Principal = Rs.2560, T = 1 1/2 = 3 half year (semi-annually),
r = 6 1/4% = 25/4%
Interest for semi-annually = (25/4) x (1/2) = 25/8%
Interest on 1st half year = (PxRxT)/100
= (2560 x 25 x 1)/(100 x 8)
= Rs.80
Principal for 2nd half year =
2560 + 80
= Rs.2640
Interest for 2nd half year = (PxRxT)/100
= (2640 x 25 x 1)/(100 x 8)
= Rs. 82.5
Principal for 3rd half year = 2640 + 82.5
= Rs.2722.50
Interest for 3rd half year = (PxRxT)/100
= (2722.50 x 25 x 1)/(100 x 8)
= Rs. 85.08
Amount at the end of 3rd year = 2722.50 + 85.08
= Rs.2807.58
Interest = 2807.58 – 2560
= Rs.247.58
Q.5 A man saves ₹4000 every year and invests it at the end of the year at 10% per annum compound interest. Calculate the total amount of his savings at the end of the third year.
Ans.
Principal = Rs.4000 , r = 10% , T = 3
Interest for 1st year = (PxRxT)/100
= (4000 x 10 x 1)/100
= Rs.400
Principal for 2nd year = (Amount at the end of 1st year + his new savings)
= 4000 + 400 + 4000
= Rs.8400
Interest for 2nd year = (PxRxT)/100
= (8400 x 10 x 1)/100
= Rs. 840
Principal for 3rd year = (Amount at the end of 1st year + his new savings)
= 8400 + 840 + 4000
= Rs.13240
Interest for 3rd year = (PxRxT)/100
= (13240 x 10 x 1)/100
= Rs.1324
Therefore,
Total amount of savings at the end of 3rd year
= Rs.13240
Q.6 Calculate the amount and the compound interest on Rs.17000 in 3 years when the rate of interest for successive years is 10%, 10%, and 14% respectively.
Ans.
Interest for 1st year = (PxRxT)/100
= (17000 x 10 x 1)/100
= Rs.1700
Principal for 2nd year = 17000 + 1700
= Rs.18700
Interest for 2nd year = (PxRxT)/100
= (18700 x 10 x 1)/100
= Rs. 1870
Principal for 3rd year = 18700 + 1870
= Rs.20570
Interest for 3rd year = (PxRxT)/100
= (20570 x 14 x 1)/100
= Rs. 2879.8
Amount = 20570 + 2879.8
= Rs.23449.8
Interest = 23449.8 – 17000
= Rs.6449.8
Q.7 The simple interest on a certain sum of money for 2 years at 10% per annum is Rs.1600. Find the amount due and the compound interest on this sum of money at the same rate after 3 years, interest being reckoned annually.
Ans.
Simple Interest = (P x R x T)/100
1600 = (P x 10 x 2)/100
(1600 x 100)/(10 x 2) = 8000 P
P = Rs.8000
Interest for 1st year = 1600/2 = Rs.800
Principal for 2nd year = 8000 + 800
= Rs.8800
Interest for 2nd year = (PxRxT)/100
= (8800 x 10 x 1)/100
= Rs. 880
Principal for 3rd year = 8800 + 880
= Rs.9680
Interest for 3rd year = (PxRxT)/100
= (9680 x 10 x 1)/100
= Rs. 968
Amount at the end of 3rd year = 9680 + 968
= Rs.10648
Interest = 10648 – 8000
= Rs.2648
Q.8 A man invests Rs.4000 for three years at compound interest. After one year the money amounts to Rs.4320. Find the amount (to the nearest rupee) due at the end of 3 years.
Ans.
Interest for 1st year = 4320 – 4000
= Rs.320
Therefore,
Interest = (P x R x T)/100
320 = (5000 x R x 1)/100
R = 8%
Principal for 2nd year = Rs.4320
Interest on 2nd year = (PxRxT)/100
= (4320 x 8 x 1)/100
= Rs.345.6
Principal for 3rd year =
4320 + 345.6
= Rs.4665.6
Interest for 3rd year = (PxRxT)/100
= (4665.6 x 8 x 1)/100
= Rs.373.248
Amount = 4665.6 + 373.248
= Rs.5038.848 = Rs.5039 (round off)
Q.9 A man borrows Rs.15000 at 14% per annum compound interest. If he repays Rs.4300 at the end of the first year and Rs.5220 at the end of the second year, find the amount of loan outstanding at the beginning of the third year.
Ans.
Interest for 1st year = (PxRxT)/100
= (15000 x 14 x 1)/100
= Rs.2100
Principal for 2nd year = 15000 + 2100 – 4300
= 17100 – 4300
= Rs.12800
Interest for 2nd year = (PxRxT)/100
= (12800 x 14 x 1)/100
= Rs. 1792
Principal for 3rd year = 12800 + 1792 – 5220
= 14592 – 5220 = Rs.9372
Therefore,
Amount of laon outstanding at the beginning of the third year = Rs.9372
Q.10 Vikram borrowed 20000 from a bank at 10% per annum simple interest. He lent it to his friend Venkat at the same rate but compounded annually. Find his gain after 2 1/2 years.
Ans.
Interest paid by Vikram for = 2 1/2 = 5/2 years
S.I = (P x R x T)/100
= (20000 x 10 x 5)/(2 x 100)
= Rs.5000
For Venkat
Interest for 1st year = (PxRxT)/100
= (20000 x 10 x 1)/100
= Rs.2000
Principal for 2nd year =
20000 + 2000
= Rs.22000
Interest for 2nd year = (PxRxT)/100
= (22000 x 10 x 1)/100
= Rs.2200
Principal for next half year =
22000 + 2200
= Rs.24200
Interest for next half year =(PxRxT)/100
= (24200 x 10 x 1)/(100 x 2)
= Rs.1210
Total interest paid by Venkat = 2000 + 2200 + 1210
= Rs.5410
Therefore,
gain by Vikram = 5410 – 5000
= Rs.410
Q.11 Sachin invests Rs.200000 for 2 years at 12% per annum compounded annually. If the interest accrued is subject to income tax at 25% at the end of each year, find the amount he received at the end of 2 years.
Ans.
Interest for 1st year = (PxRxT)/100
= (200000 x 1 x 12)/100
= Rs.24000
Tax = 24000 x 25/100 = Rs.6000
Gain after 1 year = 24000 – 6000
= Rs.18000
Principal for 2nd year =
200000 + 18000
= Rs.218000
Interest for 2nd year = (PxRxT)/100
= (218000 x 12 x 1)/100
= Rs.26160
Tax = 26160 x 25/100 = Rs.6540
Gain after 2 years = 26160 – 6540
= Rs.19620
Amount at the end of 2 year = 218000 – 19620
= Rs.237620
FAQ’s related to Applied Maths Chapter 14 on compound interest and annuity:
Q.1 What is compound interest, and how does it differ from simple interest?
Ans. Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest earned over time, resulting in exponential growth of the investment.
Q.2 What are some common mistakes to avoid when solving compound interest and annuity problems?
Ans. Common mistakes include misinterpreting the problem statement, using incorrect formulas, neglecting to convert interest rates to decimal form, and misunderstanding the frequency of compounding or payment periods. It’s essential to carefully read the problem and double-check calculations for accuracy.
Q.3 How do I calculate compound interest for a given principal, interest rate, and time period?
Ans. The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the time in years.
These are few Frequently Asked Questions relating to Applied Maths Chapter 14
In Applied Maths chapter 14, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Applied Maths Chapter 14 promises an enriching learning experience that will set you on the path to success. Applied Maths Chapter 14, we delve deep into advanced mathematical concepts that are crucial for understanding.
Hi I am Rahul Rajaji ,
This is regarding the mistake to be changed
I am Studying in class 11th
Please change the mistake in exercise 14.1 question number 2 subdivision 2 . amount of second year is 1950 + 48750 = 50700 but in your website there is an addition mistake like 1950 + 48750 + 1875 = 50700 . Its my request you Kindly change this which can confuss the students .
Thank you for correcting…!!
Good