By Richardson C.H.
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Find the present value and compound discount of $4,000 due in 10 years at 5% converted annually. Solution. 05) ~ 10 = . 00 2. 10. 35. Find the present value of $2,000 due in 8 years at 4%% converted semi-annually. Solution. 02375) 2, and n = 8. ~ 16 . 2Ji%, in Table IV, so we use logarithms to S. 81. Example 3. Find the present value of $5,000 due in 7 years with interest 6% converted semi-annually, assuming money worth 5%, Solution. We first find the maturity value of the debt the present value of this sum.
136%. stand for effective rate, j for nominal rate, and of conversions per year, then J m will is m for the be the interest on $1 for one Compound conversion period. be given by Interest and Compound Discount 39 Hence, the amount of $1 at the end of one year will (2) and the effective rate will be given We may also by the equation write be substituted H(I+Y m/ \ + for (1 in (1), i) we obtain the equation (5) This equation gives the amount of a principal rate j convertible we say that case of (5) is times per year.
Hence, to discount S for S, n, S due at i% we find the principal called the present value of S. n years (1) is Hence, to accumu- P by using (1). The principal P is also 38 Financial Mathematics Exercises 3. Find the amount of $1,000 invested 15 years at 4%. Find the amount of $1,000 invested 12 years at 6%. Accumulate $500 for 15 years at 6%. 4. Discount $800 for 20 years at 3%. 6. Find the difference between the amount of $100 at simple 1. 2. pound interest for 5 years at and at com- interest 5%.
Financial Mathematics by Richardson C.H.