If $ 5,000 is invested in an account that earns 8% interest compounded

Question

If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?

A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432

A. $ 4 
B. $ 8 
C. $ 12 
D. $ 16
E. $ 432

Praveengeol · Answer

ANS B

Solution

Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408
Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400

Difference = 5408-5400=8 $

brains · Answer

Well to make it less calculation intensive we can think in this way.

Simple interest earned after one year for 8% = 5000*8/100 =400 $

Now for CI compounded semi annually interest is 4% for six month and 4% for another six month..

For 1st Six month it will be same as Simple interest earned for 4% = 5000*4/100=200$
for next six month = interest earned on interest will be only extra which makes its CI .

Hence interest earned on next six month = 200+ 4% of 200 = 200+ 4/100*200=200+8 = 208$

So total interest at end of 1 year in CI = 200+208 = 408 $

So only 8 $ difference between CI and SI.

I would suggest to get yourself acquainted with Interest earned on Interest using basic SI approach rather than CI formula. Most of the time it comes handy

ScottTargetTestPrep · Answer

Solution:

We use the compound interest formula: A = P(1 + r/n)^nt, where P is the original principal of 5,000, r = the annual interest rate of 0.08, n = the number of compounding periods per year, which is 2, and t = the time, in years, which is 1.

The amount in the account after 1 year if the interest is compounded semi-annually is:

A = 5,000 x (1 + 0.08/2)^2 = 5,000 x 1.0816 = $5,408

The amount in the account after 1 year if the interest is simple interest is calculated by using the simple interest formula: A = P + P x r x t, where P is the principal of 5,000, r is the interest rate of 0.08, and t is the time in years, which is 1.

A = 5,000 + 5,000 x 0.08 = 5,000 + 400 = $5,400

So the former is $8 more than the latter.

Answer: B

pappal · Answer

when compounded half yearly r=4% 
hence interest= 200+200+4%of 200(Ist half interest)=408
simple interest at 8%=5k*8/100=400
so difference=$8 B

If $ 5,000 is invested in an account that earns 8% interest compounded

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If $ 5,000 is invested in an account that earns 8% interest compounded

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