Understanding Selected Topics in ANNUITY INTEREST EQUATION OF VALUES SAMPLE

PROBLEMS Wilson Cordova De La Salle University RVR-College of Business Decision Sciences and Innovation Department the amount of money paid for the use of borrowed capital or the income produced by money which has been loaned. Simple Interest Compound Interest Interest earned per period is constant for the entire term of loan. I = Prt Interest earned per period is automatically reinvested to earn more interest for the succeeding periods within the same term of loan. Maturity Value (F) accumulated amount or future worth. F = P (1 + r t )

F = P (1 + i) Determine the maturity value if P1,000 is invested for 2 years, if money is worth 10% compounded semi-annually. Present Value (P) present value equals to principal amount P = F / (1 + rt) and

P = F(1+i) Equivalent and Comparison Nominal (m>1) Rate Effective (m=1) Rate F = P ( 1 + w ) E -n F = ( 1+ j/m) m N BUSMATH 1.What effective rate is equivalent to 12% compounded quarterly?

2.What nominal rate that is compounded semi-annually is equivalent to 15% effective rate?

3.What nominal rate compounded semi-annually is equivalent to 8% converted every 2 months? an equation that shows that one set of values is equal to another set on the same comparison date. Summation of Payments = Summation of Obligations 3 simple steps to follow 1. Draw a time diagram. Write all obligations above and all payments below. 2. Choose a comparison date. 3. Bring all values to the comparison date then set the equation of values. a sequence of equal payments made at equal intervals. Annuity Certain vs Contingent Annuity Ordinary Annuity an annuity in which payments are made at the end of each interval. an annuity in which payments are made at the beginning of each interval. Annuity Due one in which the first payment is neither at the beginning nor the end of the first interval but at some later time. Deferred Annuity Derivation of both

A & S Formula Supposed X owes Y the following obligations:

5000 PhP due at the end of 1 year without interest;

6000 PhP due at the end of 3 years at 10% simple interest;

7000 PhP due at the end of 6 years at 12% compounded annually.

If X wishes to replace all these obligations by a payment of 4000 PhP at the end of 4 years and another payment at the end of 5 years, determine the size of this payment if money is worth 10% compounded semi-annually. Professional Learning Community n thank you for listening... Relationship between A & S A=R [ 1- (1+i) _____________ i ] -n [ ] _____________ (1+i) - 1 i S=R n Determine both present value and amount of a 3000 PhP annuity payable quarterly for 2 years at 8% compounded quarterly.

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