Lav If D is not the correct answer then I think this question have what can be dubbed wording issues. The first issue is that whenever compound interest is given, you want to know whether we are compounding annually, semiannually or quarterly. We also are not given how many years. If we are compounding annually then there is no difference between an SI and a CI
Example.
100 x 5% x 1 yr= $5 in interest. So we have $105 after one year.
CI= 100 (1+.05)^1= $105 after one year.
So the difference b/w CI and SI is 0 when we compound annually,which means we cannot compound annually in the given question since the difference is $25. Letting P be amount borrowed lets set up semi annual and quarter compounding as follows:
Semi Annual
CI( Componding semi) - SI = 25
(P(1+5%/2)^2(1) - P) - 5%P = 25
The general formula for compound interest is
P ( 1+r/n)^nt
P is principal, n is period of compounding and t is years. n can be 1, 2, or 4 for annual, seminannual or quarter compounding respectively. So above we take t =1 and n=2 for 1 yr and semi. We subtract P in CI case to get interest since the formula P( 1+r/n) automatically adds interest to principal.
If you solve the above, just factor P out and work with decimals you get
P= 25/.000625 = 40,000.
This is not among the answer choices.
Compounding Quarterly for 1 year
(P(1+5%/4)^4(1) - P) - 5%P = 25
P=25/.0009453=26,445!!! which is problematic b/c we should be intuitively getting an amount greater than $40,000 since we are compunding faster. This rules out quarter compounding under those terms.
So you will have to post the solution not just the OA for any choice other than D.
I go with D
Simple Interest & compound interest 4
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