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Donald plans to invest x dollars in a savings account that

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rohit8865
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink] New post   05 Jun 2016, 05:08
temp33 wrote:
IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D

Can anyone plz suggest why taking fractional values doesn't meet the ans as per my below solution
x(1+8/400)^2>x+100
x(51/50)^2>x+100
(26x/25)-x>100
x/25>100
x>2500
so ans must be E.

Thanks .
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   12 Mar 2017, 08:24
be careful when reading!
0,08 annual interest compoinded quarterly and paid in 6 months!
so the formula would be (0,08/4)^2= 4/10^(2+2)
2500 is the answer
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mikemurawski93
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   09 Apr 2017, 15:52
Hi Bunuel,

In your equation above, x(1+.02)^2 - X> 100... where did you get the -X from? The equation for compound interest is A = P (1+r/n) ^nt. I was unaware we needed to subtract an x for the correct answer or where we even got the -X from. Could you please help?
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   09 Apr 2017, 21:53
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mikemurawski93 wrote:
Hi Bunuel,

In your equation above, x(1+.02)^2 - X> 100... where did you get the -X from? The equation for compound interest is A = P (1+r/n) ^nt. I was unaware we needed to subtract an x for the correct answer or where we even got the -X from. Could you please help?


Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

x(1+.02)^2 is the final amount, while x(1+.02)^2 - x is the interest earned.
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink] New post   27 Aug 2017, 00:34
rohit8865 wrote:
temp33 wrote:
IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D

Can anyone plz suggest why taking fractional values doesn't meet the ans as per my below solution
x(1+8/400)^2>x+100
x(51/50)^2>x+100
(26x/25)-x>100
x/25>100
x>2500
so ans must be E.

Thanks .


Basically substitution is not required.
If we can calculate that the actual amount, say x turns to 1.0404 after 6 months then the actual interest is 0.0404x, which must be greater than 100.
While calculating (100/0.0404) you can realize that the value is just less than 2500.
Hence option D satisfies our condition and is the correct answer.
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink] New post   08 Sep 2017, 20:50
We can solve this without doing complex calculation since the answer choices are wide spread.
8% is the interest compounded qtrly.
let us see if we take simple interest what are the values we get.
8% of $1500= 120 and 6-month interest will be 60. even if we take the compound interest it will not touch $100
8% of $1750=same as above no need to do the calculation or keep it to the last
8% $2000=$160 and half year or 6-month return will be 80
8% of $2500=$200 6 months return will be 100-Answer.
$3000=no need to do the calculation.
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   22 May 2018, 05:37
Annual rate -8%, so quaterly rate 2%

As the CI is quaterly(3 months), for 6 months .. 2 times

x *102/100*102/100

x*1.02*1.02

x*1.0404

check the options by replacing x....result should be 100 more than the selected choice

option D....2500 * 1.0404 = 2601.... so interest is 101...
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Re: Percents question [#permalink] New post   15 Sep 2018, 12:42
CI = P(1 + r/400)^2n - x
100 = x(1 + 8/(4*100))^2 - x
solve for x to get x=2500 approx.
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   05 Aug 2019, 14:44
TheRob wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A. 1500
B. 1750
C. 2000
D. 2500
E. 3000



We can solve this using Answers.
if the annual rate is 8% then for 6 month it is 8/2=4%
DOnald need to earn $100 interest then
A) 1500- 4% of 1500= $60<100
B0 1750- 4% of 1750=$70<100
c) 2000- 4% 0f 2000= $80<100
d) 2500- 4% of 2000= $100 so answer is (D)

Hope this helps..
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   11 Jan 2020, 20:09
Sorry if this is unrelated, but where can I find the "code" or "tag" (e.g. M14-30) to this problem? I'm compiling notes on different Qs, and I'd rather not have to write the title every time.
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   31 Mar 2023, 02:12
Given: Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly.
Asked: Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

Prinicpal amount after 6 months (2 quarters) = x(1+8%/4)ˆ2
Interest = x(1+2%)ˆ2 - x = x{1.02ˆ2-1} = x{1.0404 - 1} = .404x = $100
Minimum x = $100/.404 ˜ $1000/4= $2500

IMO D
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Re: Donald plans to invest x dollars in a savings account that [#permalink] New post   31 Mar 2023, 02:43
Expert Reply
TheRob wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A. 1500
B. 1750
C. 2000
D. 2500
E. 3000


An annual rate of 8% means a quarterly rate of 2%.
In 6 months, we have two quarters i.e. two time periods. So in the first time period, 2% interest will be earned. In the second time period, 2% will be earned along with 2% of the previous interest (overall, a very small value).
So we can assume approx 4% interest earned in 6 months.

1% of 1500 is 15 so 4% is 60 - Reject
...
1% of 2000 is 20 so 4% is 80. To reach 100, we need almost another $20 which is 50% of the value of previous interest. Not correct.
1% of 2500 is 25 so 4% is 100 - This is it.

Answer (D)
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Re: Donald plans to invest x dollars in a savings account that [#permalink]
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