Question

Question 2  

Suppose you are to deposit funds into a savings account at a continuous rate of payment of $100 per year, in perpetuity. The payments will commence in 6 months.

Assuming i = 5.5%, calculate each of the following (show all working).

1. The present value now, of all future deposits made. Give your answer to the nearest cent.                                                                                          [2 marks]

2. The present value in exactly 5 years time, of all future payments made from time 6 onwards. Give your answer to the nearest cent.                                              [1 mark]

3. The present value in exactly 100 years time, of all future payments made from time 100 onwards. Give your answer to the nearest cent.                               [1 mark]

4. The accumulated value in the savings account in exactly 30 years time from now. Give your answer to the nearest cent.                                                 [2 marks]

Answer 1

a)	The present value now, of all future deposits made. Give your answer to the nearest cent.       Interest (i) 5.50% Periodic payment (PMT) 100 Pertuity (nper) 999 Present value ₹ 1,818

The present value in exactly 5 years time, of all future payments made from time 6 onwards. Give your answer to the nearest cent.

Interest (i)	5.50%
Periodic payment (PMT)	100
Pertuity (nper)	5
Present value	₹ 427

The present value in exactly 100 years time, of all future payments made from time 100 onwards. Give your answer to the nearest cent.

nterest (i)	5.50%
Periodic payment (PMT)	100
Pertuity (nper)	100
Present value	₹ 1,810

The accumulated value in the savings account in exactly 30 years time from now. Give your answer to the nearest cent.

simple chart for calculation of accumulated amount in excel is given below
year	Amount paid	interest @ 5.5%	Accumulated amount
1	100	5.50	105.5
2	100	11.00	111.00
3	100	16.50	116.50
4	100	22.00	122.00
5	100	27.50	127.50
6	100	33.00	133.00
7	100	38.50	138.50
8	100	44.00	144.00
9	100	49.50	149.50
10	100	55.00	155.00
11	100	60.50	160.50
12	100	66.00	166.00
13	100	71.50	171.50
14	100	77.00	177.00
15	100	82.50	182.50
16	100	88.00	188.00
17	100	93.50	193.50
18	100	99.00	199.00
19	100	104.50	204.50
20	100	110.00	210.00
21	100	115.50	215.50
22	100	121.00	221.00
23	100	126.50	226.50
24	100	132.00	232.00
25	100	137.50	237.50
26	100	143.00	243.00
27	100	148.50	248.50
28	100	154.00	254.00
29	100	159.50	259.50
30	100	165.00	265.00
	3,000.00	2,557.50	5,557.50