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Marcus deposited $8,000 to open a new savings account that [#permalink]

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29 Feb 2012, 17:08

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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?

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.

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.

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.

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.

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.

Bunuel,

For all CI problems if the interest is given Annually and asked Quarterly or half yearly CI , then we can just divide the Percent according our need. Tats all?

Re: Marcus deposited $8,000 to open a new savings account that [#permalink]

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Re: Marcus deposited $8,000 to open a new savings account that [#permalink]

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