1. Sally borrows X for four years at an annual eective interest rate of 8%, to be repaid with equal
payments at the end of each year. The outstanding loan balance at the end of the third year is 559.12.
Calculate the principal repaid in the rst payment. [4 marks]
2 . An annuity is paid half-yearly in arrears at a rate of KSh.18,000 per annum, for 20 years. The rate
of interest is 6% per annum eective in the rst 13 years and 7% per annum convertible quarterly for
the remaining 7 years. Calculate the accumulation of the annuity at the end of 20 years. [4 marks]
3 . A payment of KSh.24,000 is due in 8 years time in return for KSh.4,000 now, KSh.8,000 in 5 years
and KSh.X in 10 years. If i = 8%, nd KSh.X, such that the value of both options is equal. [4 marks]
4. 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. [6 marks]
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