udaymathapati wrote:

A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1440 had it been put at the rate of interest compounded annually?

1. 4.5

2. 3.5

3. 3

4. 2

5. 1

Simple interest, SI, per year

Years (5-2) = (2,000-1,400) = $600 SI in 3 years

SI per year is $600/3 = $200

Original amount?

Year 2 - 2(200): 1,400- 2(200) = $1,000

Simple interest rate:

\(\frac{200}{1000} *100\) = 20%How many years for $1,000 to be $1,440 if interest rate were compounded annually?

First year only: simple interest = interest compounded annually

End Year 1: (1,000 + 200) = $1,200

End Year 2: (1,200 * 1.2) = $1,440

OR

1,200+(.2)(1,200)=(1,200+240)= $1,440

Answer D

Alternatively,

\(A = P(1 + r)^{t}\)P = principal, r = decimal interest rate, t = time

The number "$1,440," and compound interest rate "1.2" are big hints.

\((1.2)^2 = 1.44\); principal = $1,000

Mentally I just did

\($1,000(1.2)^2 = $1,000(1.44) = $1,440\) The long way:

\($1,440 = 1,000(1 + .20)^{x}\)

\($1,440 = 1,000(1.20)^{x}\)

\(\frac{1,440}{1,000} = (1.2)^{x}\)

\(1.44 = 1.2^{x}\)

\((1.2)^1(1.2)^1 = 1.2^{x}\)

\(1 + 1 = x\)

\(x = 2\)Answer D

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