Interest problem

[metallicafan]

An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment?

A $17000
B $18000
C $19000
D $20000
E $21000

A fast way to solve it? Thanks!

[puneetkhurana2000]

29200 = x(1 + 10/100)^4.

Solving we get x = 19943.99.

Answer D.

[GMATGuruNY]

An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment?

A $17000
B $18000
C $19000
D $20000
E $21000

A fast way to solve it? Thanks!

20% interest compounded semi-annually means that 10% is earned every 6 months.
We can plug in the answers, which represent the initial investment.
Problems about compound interest tend to involve VERY ROUND numbers.
Thus, we should start with D:
1st 6 months: 20000 + 2000 = 22000.
Next 6 months: 22000 + 2200 = 24200.
Next 6 months: 24200 + 2420 ≈ 26600.
Next 6 months: 26600 + 2660 ≈ 29200.
Success!

The correct answer is D.

[shreerajp99]

Hi Mitch,

U use nos effectively while solving questions.What is ur approach when u see a quant question?How do u decide which option to be tried 1st/when to use numbers instead of variables given in the question?
I have seen that in inequalities/absolute values questions,inserting numbers can be a recipe for disaster.What's ur take on it?

Thanks,
Shreeraj

[Scott@TargetTestPrep]

An investment receives 20% annual interest compounded semi-annually for 2 years. If its final value is $29,200, approximately what was the initial investment?

A $17000
B $18000
C $19000
D $20000
E $21000

A fast way to solve it? Thanks!

We use the compound interest formula: A = P(1 + r/n)^nt, where A = the final value, P = the initial value, r = the interest rate (decimal), n = the number of compounding periods per year, and t = the number of years. We can create the equation:

29,200 = P(1 + 0.2/2)^[(2)(2)]

29,200 = P(1.1)^4

29,200 = 1.4641P

19,944 ≈ P

Answer: D