Question

Convert the constant annual effective rate 2.3443% to force of interest δ , determine the accumulated amount in your account at 31 December 2020 (ten years in total) according to the following deposit patterns. i) Deposit $5,000 per annum continuously over 10 years. ii) Deposit $5,000 continuously for the first year and keeps increasing by $1000 in the subsequent years until the yearly continuous rate of deposit achieves $9,000, then remains at $9,000 in all the following years. iii) Deposit $9,000 continuously for the first year and keeps decreasing by $500 in the subsequent years until the yearly continuous rate of deposit achieves $5,500, then remains at $5,500 in all the following years. iv) Deposit $6,000 continuously over year 2011, $6600 continuously over year 2012, $7200 continuously over year 2013, ……, and $11,400 continuously over year 2020.   
(show detailed working)

Answer 1

formulas used :-

force interest	0.023443
Year	OPTION (I)	Interest factor	option 2	option 3	option 4
1	5000	=(1+$D$1)^(10-C3)	5000	9000	=6000
2	5000	=(1+$D$1)^(10-C4)	6000	8500	=H3+600
3	5000	=(1+$D$1)^(10-C5)	7000	8000	=H4+600
4	5000	=(1+$D$1)^(10-C6)	8000	7500	=H5+600
5	5000	=(1+$D$1)^(10-C7)	9000	7000	=H6+600
6	5000	=(1+$D$1)^(10-C8)	9000	6500	=H7+600
7	5000	=(1+$D$1)^(10-C9)	9000	6000	=H8+600
8	5000	=(1+$D$1)^(10-C10)	9000	5500	=H9+600
9	5000	=(1+$D$1)^(10-C11)	9000	5500	=H10+600
10	5000	=(1+$D$1)^(10-C12)	9000	5500	=H11+600
		Amount in Option 1	=SUMPRODUCT(D3:D12,E3:E12)
		Amount in option 2	=SUMPRODUCT(E3:E12,F3:F12)
		Amount In option 3	=SUMPRODUCT(E3:E12,G3:G12)
		Amount in option 4	=SUMPRODUCT(E3:E12,H3:H12)