Jack invested $4,000 in a bond that returns 8% simple interest per

Question

Jack invested $4,000 in a bond that returns 8% simple interest per annum. John invested $4,000 into another bond that returns 8% compound interest per annum, compounded six-monthly. What was the difference between the interests earned by Jack and John over one year?

A. 0
B. 1.6
C. 3.2
D. 6.4
E. 26.4

A. 0
B. 1.6
C. 3.2
D. 6.4
E. 26.4

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vasu1104 · Answer

jack
principal = 4000
r = 8% per annum

interest = PRT / 100
4000*8 / 100 = 320

john
principal= 4000
rate = 8% compound interest per annum but compounded six monthly.
that means 4% every six months. so t= 2 and R =4%
A= p(1 + (R/100))^ t
4000  ^2

interest I = A - P
4000 ^2 - 4000
4000  
4000 
4000 
326
this is approximation.

difference between john and jack interest
326- 320 
6

so ans D

Adit_ · Answer

The calculation is right but t=2! I think you accidentally wrote it as 2 there.

vasu1104 · Answer

thanks for pointing it out. appreciate your help.

dp1234 · Answer

Traditional approach - 
SI = 4000x8/100 = 320
CI = 4000 (1.04)ˆ2 - 4000 = 326.4 
Difference CI-SI = 6.4
But the calculation of 1.04ˆ2 is tedious one for me. Solved the question in under 2min but i think i needed improvement.

Alternatively, CI will be higher than SI due to interest on interest for the first 6 months. So if SI for 1 year is 320, for 6 months will be 160. Now, finding interest on this 120 at 4% for 1 period gives 160x.04 which is 6.4.

chloreton · Answer

Jack invested 4000 @ 8% p.a. Interest earned = 320
john invested 4000 @ 8% p.a. compounded semi-annually, therefore interest earned in 1st six months is 4% of 4000 = 160 & interest earned for next six months = 160 + 4%(160) = 160+8= 168 aprox. Total interest = 160+168 =328

Therefore difference = 8 and since options are wide apart only D is close.

Note : I have assumed 4% of 160 as 5% of 160 which is easier to calculate.

Dereno · Answer

Jack invested 4000 at 8% simple interest for a year.

Interest earned = 4000 * 8% = $320.

For Compound Interest , John invested $4000 for 8% compound interest ,   compounded six months .

If it has been 8% compound interest for one year, the amount generated in both cases will be equal to $320.

But here, the interest is 8% compound interest, which is compounded every six months.

8% interest is for 1 year = 12 months.

Therefore, compounding 6 months, the interest rate becomes 4%.

4000 @ 4% interest for the  first six months  = 4000*4% = $160.

4000 @ 4% interest for the  Second six months  = 4000*4% = $160.

Since, its compound interest, the $160 generates an interest for the second 6 months @ 4% = 160*4% =  $6.4

Total compounded interest rate = $160 + $160 + $6.4 = $320 + $6.4.

What was the difference between the interests earned by Jack and John over one year ?  $6.4

Option D

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=Ip4jg5Iqjrg

Jack invested $4,000 in a bond that returns 8% simple interest per

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