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Class 12 Applied Maths Chapter 12 Solutions
Perpetuity, Sinking Funds and EMI
EXERCISE- 12.1
Q.1 Find the present value of a perpetuity of ₹900 payable at the end of each year, if money is worth 5% per annum.
Ans. R = Rs.900, i = 5% = 0.05
P = R/i
= 900/0.05
= (900 x 100)/5
= Rs.18000
Q.2 Find the present value of a perpetuity of ₹500 payable at the end of each quarter, if money is worth 8% per annum.
Ans. R = Rs.500, i = 8/4 = 2% = 0.02
P = R/i
= 500/0.02
= (500 x 100)/2
= Rs.25000
Q.3 Find the present value of a perpetuity of ₹300 payable at the beginning of every 6 months, if money is worth 6% per annum.
Ans. R = Rs.300, i = 6/2 = 3% = 0.03
P = R + R/i
= 300 + 300/0.03
= 300 + (300 x 100)/3
= Rs.10300
Q.4 Find the present value of a perpetuity of Rs.18000 payable at the end of 6 months, if the money is worth 8% p.a. compounded semi-annually.
Ans. R = Rs.18000, i = 8/2 = 4% = 0.04
P = R/i
= 18000/0.04
= (18000 x 100)/4
= Rs.450000
Q.5 What amount is received at the end of every 6 months forever, if Rs.72000 kept in a bank earns 8% per annum compounded half yearly?
Ans. P = Rs.72000, i = 8/2 = 4% = 0.04
P = R/i
P x i = R
R = 72000 x 0.04
= 72000 x 4/100
= Rs.2880
Q.6 At what rate of interest will the present value of a perpetuity of ₹300 payable at the end of each quarter be Rs.24000?
Ans. R = Rs.300, P = Rs.24000, i = x% p.a. = x/4% quarterly = x/400
P = R/i
i = R/P
x/400 = 300/24000
x = 5% p.a.
Q.7 A man wants to deposit a lump sum amount so that an annual scholarship of ₹3000 is paid. Rate of interest is 5% per annum. Calculate the lump sum amount required, if the scholarship is to start at the end of this year and continue forever.
Ans. R = Rs.3000, i = 5% = 0.05
P = R/i
= 3000/0.05
= (3000 x 100)/5
= Rs.60000
Q.8 What sum of money invested now could establish a scholarship of Rs.5000 which is to be awarded at the end of every year forever, if money is worth 8% per annum.
Ans. R = Rs.5000, i = 8% = 0.08
P = R/i
= 5000/0.08
= (5000 x 100)/8
= Rs.62500
Q.9 Rs.2,50,000 cash is equivalent to a perpetuity of ₹7500 payable at the end of each quarter. What is the rate of interest convertible quarterly?
Ans. P = Rs.250000, R = Rs.7500, i = x/4% quarterly = x/400
P = R/i
i = R/P
x/400 = 7500/250000
x = 12% p.a.
FAQ’s related to Class 12 Applied Maths Chapter 12 on Perpetuity, Sinking Funds and EMI:
Q.1 What is a perpetuity?
Ans. A perpetuity is a type of annuity that pays a fixed amount of money indefinitely. Unlike typical annuities that end after a set period, perpetuities have no end date.
Q.2 What is a sinking fund?
Ans. A sinking fund is a fund established to save money over time for a future expense or to pay off a debt. Regular contributions are made to this fund, which earns interest, to accumulate enough to meet the intended obligation.
Q.3 What are the practical applications of sinking funds?
Ans. Sinking funds are commonly used by companies to pay off debt, like bonds, to replace assets, or to fund large future expenses. Individuals may use sinking funds to save for goals like buying a car or paying for a wedding.
Q.4 What is EMI?
Ans. EMI stands for Equated Monthly Installment. It is a fixed payment amount made by a borrower to a lender at a specified date each month. EMIs are used to pay off both interest and principal over a specific period.
Q.5 What is an amortization schedule?
Ans. An amortization schedule is a table detailing each periodic payment on a loan (typically a mortgage), showing the amount of principal and interest that comprise each payment until the loan is paid off at the end of its term.
These are a few Frequently Asked Questions relating to Class 12 Applied Maths Chapter 12
In Class 12 Applied Maths chapter 12, 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, Class 12 Applied Maths Chapter 12 promises an enriching learning experience that will set you on the path to success. Class 12 Applied Maths Chapter 12, we delve deep into advanced mathematical concepts that are crucial for understanding.