Question

Q# 7: Suppose that the effective interest rate per interest period is 5%. Describe in words the meaning of the following annuity symbols and calculate them to the nearest 4 decimals a) b)(7(12)(2) c (IS 301 i 20l i

I have them all calculated; just looking for the explanations (feel free to calculate them if you want though). Thanks

Answer 1

A

Upper case S implies assured payment at the occurrence of the event. The bar on the top implies one-time payment at the time of occurrence of the event (such as death). The subscript 30 in angle mark (box) indicates period of payment of the annuity. i is the indicator of interest rate of 5%.

The overall implication of this symbol is an annuity – the annuity of ‘x’ amount will be paid at the time of death and at the end of every year thereafter for 30 years at an interest rate of i (=5%).

B

I is the interest rate and the superscript 12 indicates monthly (12 times) compounding per annum. Lower case a implies an annuity and the superscript 12 indicates monthly (12 times) payment per annum. The subscript infinity in angle mark (box) indicates period of payment of payment of the annuity. i is the indicator of interest rate of 5%.

The overall implication of this symbol is an annuity – the annuity ‘x’ shall be paid 12 times a year for infinite number of years (non-terminating) and at the end of every period at an interest rate i (=5%) which shall be compounded 12 times per annum.

C

I is the interest rate. Lower case s implies an annuity and the double dots indicate payment at the start of the year. The superscript 4 indicates quarterly (4 times) payment per annum. The subscript 20 in angle mark (box) indicates period of payment of the annuity. i is the indicator of interest rate of 5%.

The overall implication of this symbol is an annuity – the annuity ‘x’ shall be paid 4 times a year for 20 years and at the beginning of every period at an interest rate i (=5%)