Question 22616: I hope this is in the right spot. I need help with this question for my daughters homework. The question is-Gina wants to save money, so she can buy a new bike that costs $200. How much should she deposit into a savings account at 10% annual simple interest in order to have enough money to buy the bike after two years?
(use the formula A = p + prt)
Answer by AnlytcPhil(1807)   (Show Source):
You can put this solution on YOUR website! I hope this is in the right spot. I need help with this question for my
daughters homework. The question is-Gina wants to save money, so she can buy a
new bike that costs $200. How much should she deposit into a savings account at
10% annual simple interest in order to have enough money to buy the bike after
two years?
(use the formula A = p + prt)
Substitute 200 for A, .10 for r, and 2 for t
200 = p + p(.10)(2)
200 = p + .2p
200 = 1.0p + .2p
200 = 1.2p
200/1.2 = 1.2p/1.2
166.66··· = p
or $166.67, rounding up to the nearest penny.
Let's check it to see if that is correct. Checking it:
In one year the $166.67 will draw $16.66 interest (investing institutions
always round interest down to the preceding penny), so you'll then have
$166.67 + $16.66 or $183.33
In the second year the $166.67 will draw another $16.66, so you'll then
have $166.67 + $16.66 + $16.66 or $199.99.
That lacks one penny being enough, so let's add a penny and see if $166.68 will
be enough.
In one year the $166.68 will draw $16.66 interest (again rounding down to the
preceding penny), so you'll then have
$166.68 + $16.66 or $183.33
In the second year the $166.68 will draw another $16.66, so you'll then
have $166.68 + $16.66 + $16.66 or $200.00.
So the correct answer is $166.68
Edwin
AnlytcPhil@aol.com
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