Hi,
It is an interesting question.
Given: 120000 is split into two interest earning accounts.
First saving, lets call it as A = ¾(120000) = 90000
Other saving, lets call it as B = ¼(120000) = 30000
Given, total interest earned from this account is 3636 at the end of the year.
Also, given one account earns 2 percent annual interest and both compounding semi-annually.
Question: What is the rate of interest of the other account?
First task to figure out here is, which account earns two percent annual interest. Definitely it has to be the account A = 90000.
Because, lets suppose B = 30000 is the account which earns 2% annual interest which compounded semi-annually.
Compound semi-annually means two times in a year,
That’s is if “r” is the annual rate interest, then semi-annually it is r/2
(r/2)% of Amount + (r/2)% of Amount + (r/2)% of interest got in the six month period = interest amount for the year.
So interest amount earned is,
1% of 30000 + 1% of 30000 + 1% of 300 = 300 + 300 + 3 = 603
And the remaining interest should have been earned from the account A = 90000, but if you look at the answers, the rate of interest is very high and it will give you a value more than 3600.
Maybe only answer choices which may looks suitable is A = 3%, but this will give you the interest amount in decimal values. i.e.,
1.5% of 90000 + 1.5% of 90000 + 1.5% of 1350 = 1350 + 1350 + 20.25 = 2720. 25. Which contradicts the total amount 3636.
So, the 2% percent annual interest should be from the account A = 90000.
So, the interest amount should be,
1% of 90000 + 1% of 90000 + 1% of 900 = 900 + 900 + 9 = 1809.
So the remaining interest amount = 3636 – 1809 = 1827.
So, if you look at the answer choices, roughly 6/100 * 30000 = 1800. So it has to be the answer.
3% of (30000) + 3% of (30000) + 3% of 900 = 900 + 900 + 27 = 1827.
So the answer is D.
Hope this helps.
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