1. Calculate the time in days it takes for 3600 to accumulate to 4000 at:
(a) A simple rate of interest of 6% p.a. [2 marks]
(b) A compound rate of interest of 6% p.a. convertible quarterly. [2 marks]
(c) A compound rate of interest of 6% p.a. convertible monthly. [1 mark]
2. At a certain simple rate of interest, 1,000 will accumulate to 1,110 after a certain period of time. Find
the accumulated value of 500 at a simple rate of interest three fourths as great over twice as long a
period of time. [2 marks]
3. Express d(4) as a function of i(3) [3 marks]
4. You deposit 1,000 today and another 2,000 in ve years into a fund that pays simple discount at 5%
per year. Your friend makes the same deposits into another fund but at times n and 2n, respectively.
the fund credits interest at an annual eective rate of interest of 10%. At the end of 10 years, the
accumulated value of your deposits is exactly the same as the accumulated value of your friends
deposits. Calculate n [3 marks]
5. The force of interest (t) at time t is at+bt2 where a and b are constants. An amount of 1000 invested
at time t = 0 accumulates to 1500 at time t = 5 and 2300 at time t = 10. Determine the value of a
and b. [5 marks]
6. The force of interest,(t); is a function of time and at any time t, measured in years, is given by the
formula:
(t) =
8<
:
0:06 0 t 5
0:01(t2 ?? t) 5 < t
(a) Calculate the present value of a unit sum of money due at time t = 10. [4 marks]
(b) Calculate the eective rate of interest over the period t = 9 to t = 10. [3 marks]
(c) In terms of t, determine an expression for v(t), the present value of a unit sum of money due
during the period 0 < t 5. [1 mark]
(d) Calculate the present value of a payment stream paid continuously for the period 0 < t 5,
where the rate of payment, (t), at time t, is e0:04t. [4 marks]
7. You are given that the nominal rate of discount per annum convertible every 2 months is 15%. Calculate
the product of the equivalent nominal rate of interest per annum convertible every three months i(4)
and the force of interest . [6 marks]
8. A fund is earning 7% simple interest. Find the year when this will be equivalent to an eective rate
of 4:7%. [3 marks]
9. June borrows KSh.50,000 for 10 years at an annual eective interest rate of 10%. She can repay this
loan using the amortization method with payments of KSh.8,137.25 at the end of each year. Instead,
June repays the KSh.50,000 using a sinking fund that pays an annual eective interest rate of 14%.
1
STA 2191 Jane Akinyi Aduda
The deposits to the sinking fund are equal to KSh.8,137.25 minus the interest on the loan and are
made at the end of each year for 10 years. Determine the balance in the sinking fund immediately
after repayment of the loan. [5 marks]
10. 1000 is deposited into Fund X, which earns an annual eective rate of 6%. At the end of each year,
the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year,
the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y ,
which earns an annual eective rate of 9%. Determine the accumulated value of Fund Y at the end of
year 10. [6 marks]
11. Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the rst month, 4 at
the end of the second month, and for each month thereafter the payment increases by 2. The nominal
interest rate is 9% convertible quarterly. Calculate X. [6 marks]
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