Annuities - pension plan
1. How many annuities will you obtain and for how long, if an annuity
corresponds to 789.00 and every annuity is paid two times in one month.
Further, you know that it is an ahead pension, you have budged of
135,250.64 and the ﬁnancial institution oﬀers you 1,8 % p. q and counts
interest twenty four times in a year.
(24 annuities, 10 years)
2. Solve the previous example if all conditions are the same, except ﬁnancial
sources. Now lets have the available budged 136,000.00.
(241 ordinary annuities, PVa242=364.8989, FVa142=753.3527)
3. How much sources do you need to provide a regular pension paid every
two days (after payment). The pension corresponds to 10 USD and the
pansion plan is for 12 years. The pension fund gives you 3 % p. a. and
the interest is calculated every 20 days.
(18,140.47)
4. Specify the amount you need for an inﬁnite pension with regular annuity
of 32,000.00, paid at the end of every month. You know that the
interest rate corresponds to 2 % p. s. For the solution consider continous
interest with an identical impact on capital. After you estimate
the budged provide a proof.
(9,679,692.00)
5. What amout of money you need to provide an inﬁnite pension that
will be paid at the begining of avery quarter. The ﬁnancial institution
oﬀers you 0.7 % p.m. and calculates the interest twelve times a year.
The amount of annuity is 47,000.00.
(B0=6,761,286.00)
6. Solve the previous example using the concept of continous interest with
the same impact on capital (use re and f).
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7. How much will be your pension paid monthly at the end of every
month? The pension plan is estimated for ten years. When you are
25 you start to create over next 15 years a reserve for your pension..
The saving institution promises you 1 % p. s. with monthly interest
period and you will save regularly annuity in the amount of 500 at the
end of every quarter. After you ﬁnished your saving process you move
your money to a pension fund. The pension fund will start paying you
a retirement when you are 60. The fund guarantees you 3.7 % p. a.
and the interest is calculated twice a year.
(a=724.1746)
8. How many ordinary annuities can you provide with your pension plan
and how much will be the last extraordinary annuity? For the pension
plan you have a budget of 1,000,000.00, the ﬁnancial institution
promises you 3 % p. a. and calculates interest every two months and
the pension is paid 3 times in a year. The pension in the amount of
32,000.00 is paid after.
(37 annuities of 32,000.00 plus 1 extraordinary annuity
(PVa38=14,851.45, FVa38=17,950.61)
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