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?
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.
Hope it's clear.
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?