Question

In order to have money available for replacing their family vehicle, a couple planned to have $220,000 available
in 10 years by investing in a global mutual fund. If they plan to increase their savings by 10% each year, how
much must they invest in year 1 if they expect to earn 10% per year on their investments?

Answer 1

Supose year 1 investment is $ 1 which is their saving in year 1.
Future value of savings:
Year	Investment	Future Value in year 10
a	b	c=b*(1.1^(10-a))
1	$    1.00	$    2.36
2	$    1.10	$    2.36
3	$    1.21	$    2.36
4	$    1.33	$    2.36
5	$    1.46	$    2.36
6	$    1.61	$    2.36
7	$    1.77	$    2.36
8	$    1.95	$    2.36
9	$    2.14	$    2.36
10	$    2.36	$    2.36
		$   23.58
Now, as per question,
future value of savings in year 10				=	$2,20,000
So, year 1 required saving				=	$2,20,000	/	$   23.58
				=	$9,330.15
Thus, required investment in year 1 is				$9,330.15