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.