FM for Actuaries

30 CHAPTER 1
1.7 It is given that i(t) =0.01 + 0.005t.
(a) Find a(t) for t beinganinteger.
(b) If the principal is $100, find the total amount of interest earned in year
3, 4 and 5.
1.8 Which of the following is a valid accumulation function?
(a) a(t) =t 2 +2t +2,
(b) a(t) =t 2 − 2t +1,
(c) a(t) =t 2 +2t +1.
1.9 If d (4) =0.0985, find
(a) i,
(b) d (2) ,
(c) r (4) ,
(d) δ,
(e) a(t).
1.10 A security is sold at a discount of 7%, compounded semiannually. Find the
effective rate of interest.
1.11 Prove that i − d = id by using formulas (1.30) and (1.31). What does this
relation tell you?
1.12 $1,500 is deposited into a savings account that pays 3.5% interest with
monthly compounding. What is the accumulated amount after four and a
quarter years? What is the amount of interest earned over this period?
1.13 $10,000 is deposited into a savings account that earns 3% per annum compounded
quarterly.
(a) How much interest will be credited in the second month?
(b) How much interest will be credited in the second year?
1.14 Using the rule of 72, calculate the approximate number of years for an initial
principal to double if the annual effective rate of interest is 4%. Compare
your answer with the true value.