Basic Concepts of Financial Mathematics Applied Maths - Basic Concepts of Financial Mathematics

The present value of an annuity is the worth of an annuity _______________ .

Which of the following is not true regarding an annuity due ?

Time value of money supports the comparison of cash flows recorded at different time period by

Relationship between annual nominal rate of interest and annual effective rate of interest, if frequency of compounding is greater than one:

A machine can be purchased for ₹ 50000. Machine will contribute 12000 per year for the next five years. Assume borrowing is 10% per annum compounded annually Determine whether machine should be purchased or not.
Given P(5,0.1) = 3.79079

ABC Ltd. wants to lease out an asset costing ₹ 36,000 for five years has fixed rental of ₹ 105000 per annum payable annually starting from the end of first year. Suppose rate of interest is 14% per annum compounded annually on which money can be invested by the company. Is this agreement favourable to the company ?
(Given, P(5,0.14) = 3.43308 )

Write the relationship between present and future value of an annuity regular.

Write four applications of ordinary (regular) annuity.

What is the difference between annuity regular and annuity due?

₹ 1000 is invested every 3-months at 4.8% compounded quarterly. How much will the annuity be worth in 2 years?

₹ 5000 is paid every year for three years to pay off a loan. What is the loan amount if interest rate be 14% per annum compounded annually ?

What is the monthly equivalent interest rate to a quarterly interest 2.5% ?

₹ 5000 is invested in a Term Deposit Scheme that fetches interest 6% per annum compounded quarterly. What will be interest after one year ? What is effective rate of interest ?

₹ 16000 invested at 10% p.a. compounded semi-annually amounts to ₹ 18522. Find the time period of investment.

(a) Anil bought a TV costing ₹ 13000 by making a down payment of ₹ 3000 and agreeing to make equal annual payment for three years. How much would be each payment if the interest on unpaid amount be 14% compounded annually ?
(b) Experts say that the baby boom generation (Indians born between 1946 and 1960) cannot count on a company pension or social security to provide comfortable retirement, as their parents did. It is recommended that they start to save early and regularly. Mahesh, a baby boomer, has deposit ₹ 200 each month for 20 years in an account that pays interest of 7.2% compounded monthly.
(i) How much will be in the account at the end of 20 years?
(ii) Mahesh believes he needs to accumulate ₹ 130,000 in the 20 years period to have enough for retirement. if he can not get higher rate to produce ₹ 130,000 in 20 years. To meet the goal, he must increase her monthly payment. What payment should he make each month? Given that (1.006) ²⁴⁰ = 4.2026

(a) ₹ 200 is invested at the end of each month in an account paying interest 6% per year compounded monthly. What is the future value of this annuity after 10th payment? Given that (1.005)¹⁰ = 1.0511 deg
(b) Find the present value of ₹ 10,000 to be required after 5 years if the interest rate be 9%. Given that (1.09)⁵ = 1.5386
(c) Sneha borrows ₹ 500000 to buy a house. If she pays equal installments for 20 years and 10% interest on outstanding balance what will be the equal annual installment ? Given that ( 1.10)²⁰ =6.7274

Leela is an athlete who believes that her playing career will last 3 years.
(a) To prepared for future, she deposits ₹ 24,000 at the end of each year for 3 years in an account paying 6% compounded annually. How much will she have on deposit after 3 years ? Also, find the value of interest earned.
(b) Instead of investing ₹ 24,000 at the end of each year, suppose Leela deposits ₹ 80,000 at the end of each year for 3 years in an account paying 5% compounded monthly. How much will she have on deposit after 3 years? Also, find the value of interest earned.

(a) A man purchased a house valued at ₹ 300000. He paid ₹ 200000 at the time of purchased and agreed to pay the balance with the interest at 12% per annum compounded half yearly in 20 equal half yearly installments. If first installment is paid after six months from the date of purchase than find the amount of each installment. [Given that (1.06)²⁰20 = 3.2071 ]
(b) A person invests ₹ 500 at the end of each year with a bank which pays interest at 10% p.a. C.I. annually. Find the amount standing to his credit one year after he has made his yearly investment for the 12^th time.
[Given that (1.1) ¹² = 3.1348 ]

(a) A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest in how many years?
(b) Compound interest on a sum of money you 2 years at 4% per annum is 2448. Find simple interest on the same sum of money at the same rate of interest for 2 years.

A series of equal payments made at equal intervals is known as _______________ .

An annuity due is an annuity where the payments occurs at _______________ .

An annuity that occurs forever is known as a(n) _______________ .

The process of calculating future value of money from the present value is classified as _______________

If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be _______________

A mortgage of ₹ 190,000 is required to purchase a house. The mortgage will be repaid with equal monthly payments over 25 years at 8% compounded monthly.
(a) What is the monthly payment?
(b) What is the total interest paid over the 25 years ? Given that, (1.006)³⁰⁰300 = 7.3402

A machine with useful life of seven years costs ₹ 10,000 while another machine with useful life of five years costs ₹ 8000. The first machine saves labour expenses of ₹ 1900 annually and the second one saves labour expenses of ₹ 2200 annually. Determine preferred course of action. Assume cost of borrowing as 10% compounded per annum.
Given, P(7,0.1) = 4.86842 P(5,0.1) = 3.79079

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is 1. Find the sum.