1. Chapter 4. Simple and Compound Interest including Annuity – Applications Why is interest paid? Time value of Money Opportunity Cost Inflation Liquidity Preference Risk Factor Definitions Interest – is the price paid by a borrower for the use of a lender’s money Principal – is the initial value of lending Rate of Interest – the percentage rate at which the interest is charged for a defined length of time for use of principal Accumulated Amount – is the final value of an investment Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
2. Chapter 4. Simple and Compound Interest including Annuity – Applications Simple Interest I = P.I.t A = P + I = P (1 + i.t) I = A – P Where A = Accumulated Amount P = Principal i = annual interest rate in decimal I = Amount of Interest t = time in years Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
3. Chapter 4. Simple and Compound Interest including Annuity – Applications Compound Interest An = P (1 + i)n where i = Annual rate of interest / Number of conversion periods per year n = number of periods An = Accumulated Amount P = Principal Compound Interest = An – P = P [(1+i)n – 1] Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
4. Chapter 4. Simple and Compound Interest including Annuity – Applications Effective Rate of Interest I = P.E.T. Where I = amount of interest E = Effective rate of interest in decimal T = time period P = Principal Amount E = (1+i)n – 1 Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
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6. Time interval between two consecutive payments (or receipts) must be the sameRevision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
7. Chapter 4. Simple and Compound Interest including Annuity – Applications Annuity Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
8. Chapter 4. Simple and Compound Interest including Annuity – Applications Future Value Future value is the cash value of an investment at some time in the future. F = C.F. (1 + i)n Where F = Future Value CF = Single Cash Flow Future value of an annuity (regular) If A be the periodic payments the future value A(n i) of the annuity is given by A(n i) = Future value of Annuity (immediate) Calculating the future value of the annuity due involves two steps Step 1: Calculate the future value as though it was an ordinary annuity Step 2: Multiply the result by 1+i Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
9. Chapter 4. Simple and Compound Interest including Annuity – Applications Present Value Present value and future value are reciprocal to each other. The present value P of an amount An due at the end of n interest period at the rate of i per interest period may be obtained as: P = An / (1 + i)n Present Value (V) of Annuity Regular (A) of n periods is the sum of the present value of payments V = A / (1 + i)1 + A / (1 + i)2 +A / (1 + i)3…. . +A / (1 + i)n Alternately A = V / P (n i) Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
10. Chapter 4. Simple and Compound Interest including Annuity – Applications Present value of an Annuity (immediate) is calculated in two steps Step 1: Compute the present value of the annuity as if it were a annuity regular for one period short (n – 1) Step 2: Add initial cash payment / receipt to the Step 1 value Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
11. Chapter 4. Simple and Compound Interest including Annuity – Applications Sinking Fund Sinking Fund is a fund credited for a specified purpose by way of sequence of periodic payments over a time period at a specified interest rate. Interest in compounded at the end of every period. Size of the sinking fund deposit is computed from A = P.A(n i) where A is the amount to be saved, P the periodic payment, n the payment period. Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
12. Chapter 4. Simple and Compound Interest including Annuity – Applications Applications of Present Value Leasing Leasing is a financial agreement under which the owner of the asset (lessor) allows the user of the asset (lessee) to use the asset for a defined period of time (lease period). Present Value concept can be used to find whether giving out an asset on lease is favorable for not. Capital Expenditure (investment decision) Purchase of an asset falls under capital expenditure. Present value concept can be used to calculate whether it is favorable to invest in an asset or not (if inflows from benefits > outflows for purchase) Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
13. Chapter 4. Simple and Compound Interest including Annuity – Applications Applications of Present Value Valuation of Bonds A bond is a debt security in which the issuer owes the holder a debt and is obliged to repay the principal and interest. Present value concept helps to decide whether or at what rates bonds should be purchased to achieve a specified rate of return. Revision Notes – Quantitative Aptitude www.cptsuccess.com Page 1 of 1
