kanigmat011 wrote:
esledge wrote:
I'm not sure this method dodges formulas as much as you want, but here goes:
10% of the initial deposit is $600, and the account has already earned $125+$130+$145 = $400. Must make $200 in the last quarter, and the balance at that point is $6000+$400 = $6400.
This method is called Benchmarking:
If 1% (annual rate) were earned on $6400, that would be $64 a year or $64/4 = $16 per quarter.
How many $16 payments (i.e. 1 percent payments) must this account earn to collect $200? $200/$16 = 12.5 of the 1% payments, or 12.5%.
Alternatively, you could benchmark using 10% (annual rate). That would give us $640 a year or $160 per quarter (not enough, but A,B, and C are wrong for sure). $160 plus $40 (or 1/4 of $160) is what we need. Thus, 10% + (1/4)(10%) = 12.5%
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Hi Esledge
Thanks for wonderful explanation,but i have a confusion here.
If we use the normal interest computation formula Interest=( Amount *Rate of Interest *Duration)/100
We get( 6000*R*0.25)/100=125
R=8.3
Can you through some light why this technique is not applicable here?
Hi
kanigmat011 that will not applicable because you are using the formula for Simple Interest calculation where as the question asks for Compound Interest working. Now, how do we know that the question deals with CI? Because the interest earned on the account was reinvested quarterly; thus the interest earned during the previous quarters will also further earn interest on them.
In case of Simple Interest, the interest earned during the previous quarters do not earn interest on them, only the principal does. Hence, the technique you are using would not apply here.
The other way to solve this problem would be:
Amount of interest to be earned in the last quarter= 6000* 0.10 - (125+130+145) = 200
Principal balance in the account = 6000 + 400 = 6400
Hence, quarterly interest rate = \(\frac{200}{6400}\) * 100 = 3.125%
So, the annual interest rate = 3.125% * 4 = 12.5%
Hope it helps!
Regards
Harsh
But as per my understanding SI or CI for first initial year is same.
So here in this case 1st quarter CI on amount of 6000 should be same as SI on amount of 6000 . So equating that we get rate of interest as