By A. H. Pollard (Auth.)
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Additional resources for An Introduction to the Mathematics of Finance
402 that is, 7 years 147 days from now. 7-3 T h e equation of value is . . 47 7-4 T h e equation of value is . . 104 = la^ + IOOt; 9 at some u n k n o w n rate of interest. T h e R . H . S . a. T h e R . H . S . a. By interpolation, R . H . S . a. a. a. and the new equation of value . . B. T h e "capital gain" is here a loss of $4 on maturity which is an allowable deduction for tax purposes. e. a. a. a. a. a. '. V. 93 8-3 T h i s could also be obtained by interpolation, b u t it is simpler to use the result of Exercise 8-2.
Ii) W h a t is the a m o u n t of loan outstanding after 15 years? (iii) If the company expects to pay a n n u a l compound bonuses at 2 % based on the a m o u n t of policy and declared bonuses, what is the a m o u n t of the insurance cover at the end of 15 years? 11 (ii) T h e a m o u n t still owing after 15 years equals the then present value of his future payments on the loan. 02) » = $10,767 COMPOUNDING MORE FREQUENTLY THAN ANNUALLY 47 EXERCISES 8-1 W h a t is the effective a n n u a l rate of interest correspond, ing to .
Iii) Find the real m o n t h l y c o m p o u n d interest r a t e involved and determine the corresponding effective a n n u a l rate. (iv) Draw u p a schedule as in (ii) b u t giving the the true figures. SOLUTIONS TO EXERCISES 1-1 I = $10 Ρ = $490 365 /. a. ·. '. it will take 49 days 1-4 N u m b e r of days = 29 + 16 = 45 45 / . a. ". a. a. *. 68 1-9 Let Ρ = a m o u n t asked for. T h e n Ρ m i n u s the interest in advance equals $1000. ·. V. V. *. 75 By interpolation /. a. a. 02 2-5 As the rate of interest earned on the investment (6%) is the same as that used in working the present value in exercise 2-4, we may simply add interest to that present value.