Question

1. If ? = 6%, and ? = 10, find ?̅15| ̅̅̅̅̅ and ?̅ 15| ̅̅̅̅̅.

2. Find the present value of an annuity due with 17 annual payments of 100, 96, 92, … ,36. Use effective annual rate of 4%.

3. At any moment ?, a continuously-varying continuous 5-year annuity makes payments at the rate of ? 2 per year at moment ?. The force of interest is 5%. Determine the present value of this annuity

Answer 1

Answer-1

i = 6% or 0.06

n = 10

a15 or Present value of the Annuity payment of 15 =

=> a15 Present value of the Annuity payment of 15 =

=>a 15 = 110.4013058 or 110.40 (approx)

S15 of Future value of annuity payment of 15 =

=>S15 of Future value of annuity payment of 15 =

=>S 15 = 197.7119241 OR 197.71(Approx)

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Answer-2

Annuity Due means the payment are to be made at the begin of the year.

	A	B		A*B
Year	Payment	PVF@4%		Present value of the payment
0	100	1.00000000	1/(1.04)^0	100.00000
1	96	0.96153846	1/(1.04)^1	92.30769
2	92	0.92455621	1/(1.04)^2	85.05917
3	88	0.88899636	1/(1.04)^3	78.23168
4	84	0.85480419	1/(1.04)^4	71.80355
5	80	0.82192711	1/(1.04)^5	65.75417
6	76	0.79031453	1/(1.04)^6	60.06390
7	72	0.75991781	1/(1.04)^7	54.71408
8	68	0.73069021	1/(1.04)^8	49.68693
9	64	0.70258674	1/(1.04)^9	44.96555
10	60	0.67556417	1/(1.04)^10	40.53385
11	56	0.64958093	1/(1.04)^11	36.37653
12	52	0.62459705	1/(1.04)^12	32.47905
13	48	0.60057409	1/(1.04)^13	28.82756
14	44	0.57747508	1/(1.04)^14	25.40890
15	40	0.55526450	1/(1.04)^15	22.21058
16	36	0.53390818	1/(1.04)^16	19.22069
			Total	907.64390

hence PV of the annuity payment = 907.64390

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