Question

There are two accounts. The first pays 10% per year simple interest and the second pays 5% per year interest compounded quarterly. Initially, the first account pays more interest but at some point in time the second account will pay more annual interest. How long before the second account earns more annual interest?

Answer 1

Answer:

Normally for the above question, we have 2 different ways for to find the answer.

1.Using Formula

2.Using Calculator individually (TRADITIONAL) (Not Need)

1.Using Formula :​​​​​ ;

Simple Interest

Amount = Principle * Rate of Interest

Compound Interest

Amount(A) = Principle(P) (1+r/n)^n(t)

Here, r = Rate of Interest (Decimal)

n = No of times interest is compounded

t = No of Years

If We are need Only interest amount ,then INTERSET = P(1+r/n)^n(t)- P

Let us take an Example, If we are deposit $100 into 2 accounts (Based on above)

Account -1 @ 10% p.a Simple Interest

Account -2 @ 5% p.a Interest Compounded Quarterly

Account -1 @ 10% p.a Simple Interest

In 1^st Year ,

Interest = $100*10% = $10

In 2^nd Year,

Interest =$100*10% = $10 (Only)

Account -2 @ 5% p.a Interest Compounded Quarterly

In 1^st Year ,

Interest =100(1+0.05/4)⁴⁽¹⁾ - 100 = 100(1.05) - 100 = $5 (only Taking 2 decimals )

In 2^nd Year,

Amount =$105 (Because Compounded Interest Included in Principle)

Interest =105(1+0.05/4)⁴⁽¹⁾ - 105 = 105(1.05) - 100= 110.25 - 100  = $10.25 (only Taking 2 decimals )

Compared to Account -1 & Account -2 ,

Interest amount of Account-2 is Increased from 2^nd Year Last Quarter compared to Account-1 even though Rate of interest is not Changed.

i.e Interest on Account -2 - Interest on Account -1 = $10.25 - $10 = $0.25 (approx) {From Year 2 ,4 Quarter Onwards)

So,on the basis of above, 2 Years time is needed to Account-2 for earns more annual interest compared to

Account-1.

THANK YOU !