Question

Consider an annuity with an inital value of R120000 and monthly withdrawls of R3400. The annuity has an interest rate of 2% per month compounded quarterly (4 times per year). Construct a model for the remaining value in the annuity after n steps. Determine if the annuity grows, is in equilibrium or depletes over time.

Answer 1

There will be decreasing annuity as per following model

Month	Amount	Interest	Withdraw	Closing
Jan-20	120,000			120,000
Jan-20	120,000	2,400	3,400	119,000
Feb-20	119,000	2,400	3,400	118,000
Mar-20	118,000	2,314	3,400	116,914
Apr-20	116,914	2,338	3,400	115,853
May-20	115,853	2,317	3,400	114,770
Jun-20	114,770	2,251	3,400	113,621
Jul-20	113,621	2,272	3,400	112,493
Aug-20	112,493	2,206	3,400	111,299
Sep-20	111,299	2,183	3,400	110,082
Oct-20	110,082	2,202	3,400	108,884
Nov-20	108,884	2,178	3,400	107,662
Dec-20	107,662	2,112	3,400	106,373
Jan-21	106,373	2,127	3,400	105,101
Feb-21	105,101	2,102	3,400	103,803
Mar-21	103,803	2,036	3,400	102,438
Apr-21	102,438	2,009	3,400	101,048
May-21	101,048	2,021	3,400	99,668
Jun-21	99,668	1,955	3,400	98,223
Jul-21	98,223	1,964	3,400	96,788
Aug-21	96,788	1,898	3,400	95,286
Sep-21	95,286	1,869	3,400	93,755
Oct-21	93,755	1,875	3,400	92,230
Nov-21	92,230	1,845	3,400	90,675
Dec-21	90,675	1,778	3,400	89,053
Jan-22	89,053	1,781	3,400	87,434
Feb-22	87,434	1,749	3,400	85,783
Mar-22	85,783	1,682	3,400	84,065
Apr-22	84,065	1,649	3,400	82,314
May-22	82,314	1,646	3,400	80,560
Jun-22	80,560	1,580	3,400	78,740
Jul-22	78,740	1,575	3,400	76,915
Aug-22	76,915	1,509	3,400	75,023
Sep-22	75,023	1,471	3,400	73,095
Oct-22	73,095	1,462	3,400	71,157
Nov-22	71,157	1,423	3,400	69,180
Dec-22	69,180	1,357	3,400	67,137
Jan-23	67,137	1,343	3,400	65,079
Feb-23	65,079	1,302	3,400	62,981
Mar-23	62,981	1,235	3,400	60,816
Apr-23	60,816	1,216	3,400	58,633
May-23	58,633	1,173	3,400	56,405
Jun-23	56,405	1,106	3,400	54,112
Jul-23	54,112	1,082	3,400	51,794
Aug-23	51,794	1,036	3,400	49,430
Sep-23	49,430	969	3,400	46,999
Oct-23	46,999	940	3,400	44,539
Nov-23	44,539	891	3,400	42,030
Dec-23	42,030	824	3,400	39,454
Jan-24	39,454	789	3,400	36,843
Feb-24	36,843	737	3,400	34,180
Mar-24	34,180	670	3,400	31,450
Apr-24	31,450	629	3,400	28,679
May-24	28,679	574	3,400	25,853
Jun-24	25,853	507	3,400	22,960
Jul-24	22,960	459	3,400	20,019
Aug-24	20,019	400	3,400	17,020
Sep-24	17,020	334	3,400	13,954
Oct-24	13,954	279	3,400	10,833
Nov-24	10,833	217	3,400	7,649
Dec-24	7,649	150	3,400	4,399
Jan-25	4,399	88	3,400	1,087
Feb-25	1,087	22	3,400	-2,291

The present value may also be computed by using the Payout annuity formula