PENSION PLAN
Infinite annuities
(Interest period = payment period)
• How much money (budget...B) you need for an infinite pension paid four times annually, if the interest rate is 2.1 % p.q. and the bank calculates the interest quarterly The pension is paid ahead (at the begining of a payment period) and the amount of the pension is 500, 00.
B = 500 * -—±t—, 1-TPfr
whre the q = , , q;031 ,
2
since the interest rate is for 6 months and the interest period is a quarter i.e. 3 months.
• ... the pension is paid after (at the end of a payment period).
B = 500 * —
(Interest period > payment period)
• How much money you need to assure an infinite pension paid monthly with in the amount of 150,00? The pension fund offers you an interest rate of 8% p. a. and the interst is calculated
i
semiannualy, ie. every sixth month. It is ahead pension.
B = 150*6*(l + f±±*5f)*i
• ... the pension is paid after.
b = 150 * 6 * (1 + y * *f) * i
Note: 8 % is for one year and the interest period is 6 months, so 2^5.
(Interest period < payment period)
• What is the budget that will assure you an infinite ahead-paid pension of 3000.00 once a year? The financial institution promises 7 % p. a. and the interest period is one month.
b = 3000 *      \ 2
w
• ... the pension is paid after.
b = 3000 * (Jw)12 * rHns
i-L , 0.07J
Note: the monthly interest rate is ^jSp, thus the q for the sum of geometric serie is q = o.ot)12'
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2