You have decided to create a perpetual fund to support the Boston Harbor Islands and would...

You have decided to create a perpetual fund to support the Boston Harbor Islands and would like the first payment to be made in 5 years. Interest rates are 6% and you would like the payments to increase by 2% each year. How much should you invest today if you want the first payment to be $15,000 in 5 years?

How should I solve this using an hp10bii+ calculator? Could you please show me the steps?

Expert Solution

A	B	C	D	E	F	G	H	I	J	K	L	M
2
3		First payment starts at year	5
4		First payment value	$15,000
5		Growth rate of payment	2%
6		Interest rate	6%
7
8		The amount required today will be the present value of future cash flows.
9		Year	0	1	2	3	4	5	6	…
10		Payment						$15,000	$15,300	$15,606	=J10*(1+$D$5)
11
12		Present value of payments at year 4	=Present value of growing perpetuity at year 4
13			=$15,000 / (6%-2%)
14			$375,000.00	=D4/(D6-D5)
15
16		Present value of payments	=$375,000*(P/A,6%,4)
17			=$375,000 / (1+6%)⁴
18			$297,035.12	=D14/((1+D6)^H9)
19
20		Hence the amount to be invested today is	$297,035.12
21

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