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29 Feb 2012, 18:08
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:33) correct
21%
(02:00)
wrong
based on 1256
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Marcus deposited $8,000 to open a new savings account that earned
five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?
(A) $8,200
(B) $8,205
(C) $8,400
(D) $8,405
(E) $8,500
(A) $8,200
(B) $8,205
(C) $8,400
(D) $8,405
(E) $8,500
Guys - I know a very simple question. But, I am not getting the right answer. WHy?
I am using A = P(1+R/200] \(^ 2n\)
A = 8000 (1+0.05/200) ^ 2 * 6/12 = > 40(200.05) ^ 1 = 8002. So where I have got this wrong?
I am using A = P(1+R/200] \(^ 2n\)
A = 8000 (1+0.05/200) ^ 2 * 6/12 = > 40(200.05) ^ 1 = 8002. So where I have got this wrong?
29 Feb 2012, 23:39
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Marcus deposited $8,000 to open a new savings account that earned
five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?
(A) $8,200
(B) $8,205
(C) $8,400
(D) $8,405
(E) $8,500
There is indeed a formula to calculate final balance for compounded interest (check here: math-number-theory-percents-91708.html) though there are at least two shorter ways to solve this problem.
Approach #1:
5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.
For the first 6 moths interest was 2.5% of $8,000, so $200;
For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of $200, so $200+$5=$205;
Total interest for one year was $200+$205=$405, hence balance after one year was $8,000+ $405=$8,405.
Answer: D.
Approach #2:
If the interest were compounded annually instead of semi-annually then in one year the interest would be 5% of $8,000, so $400. Now, since the interest is compounded semi-annually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $400, only answer choice D fits.
Answer: D.
Hope it's clear.
(A) $8,200
(B) $8,205
(C) $8,400
(D) $8,405
(E) $8,500
There is indeed a formula to calculate final balance for compounded interest (check here: math-number-theory-percents-91708.html) though there are at least two shorter ways to solve this problem.
Approach #1:
5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.
For the first 6 moths interest was 2.5% of $8,000, so $200;
For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of $200, so $200+$5=$205;
Total interest for one year was $200+$205=$405, hence balance after one year was $8,000+ $405=$8,405.
Answer: D.
Approach #2:
If the interest were compounded annually instead of semi-annually then in one year the interest would be 5% of $8,000, so $400. Now, since the interest is compounded semi-annually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $400, only answer choice D fits.
Answer: D.
Hope it's clear.
General Discussion
29 Feb 2012, 19:00
Kudos
Bookmarks
This is a much simpler problem. I have never used exponents in calculating interest...
Compounding period is half a year so R = 0.05 * 1/2 = 0.025
8000 * (1+ 0.025) = 8200 = total at 1/2 year
8200 * (1+ 0.025) = 8405 = total at year-end
Shortcut = figure total at year end for annually compounding interest... 8000 * (1 + .05) = 8400. More frequent compounding results in ever-so-slightly increased totals so 8405 fits.
Compounding period is half a year so R = 0.05 * 1/2 = 0.025
8000 * (1+ 0.025) = 8200 = total at 1/2 year
8200 * (1+ 0.025) = 8405 = total at year-end
Shortcut = figure total at year end for annually compounding interest... 8000 * (1 + .05) = 8400. More frequent compounding results in ever-so-slightly increased totals so 8405 fits.
