An investment receives 20% annual interest compounded semi-annually fo

Question

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. $17,000
B. $18,000
C. $19,000
D. $20,000
E. $21,000

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lorenz955 · Accepted Answer

the interest is compounded semi-annually so 10% every 6 months for 4 periods.

1.1x after 6 months (x+10%x)
1.21x after a year (1.10x+10%1.10x)
1.33 x after one year and six months
1.46x after two years

1.46x=29200--->x=29200/1.46=20000

hope it helps.

Archit3110 · Answer

from given info
29200 = x * ( 1+10/100)^4
solve for x = ~ 20,000
IMO D

saukrit · Answer

Le x be the principal

x* 1.1^4 =29200
x= \frac{29200}{14641} *10000 
=~ 20000

Hence D

superczan · Answer

Is there a quick way to solve for principal. I know the formula and know the cocept too but could not figure out 29200/2.2^4 = ?

lfernandochg1990 · Answer

I think the same... I think it's very time consuming.. can somebody please give any tip to solve this fast? Thanks!

ScottTargetTestPrep · Answer

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)^

29,200 = P(1.1)^4

29,200 = 1.4641P

19,944 ≈ P

Answer: D

metalhead2593 · Answer

The formula is T (initial amount)*(1.1)^4 = 29200

now, we know that 11^2 = 121. So 1.1^4 = 1.21^2 = 1.4641 (sr, can't get a shortcut for this, you have to memorize the value of 11^2 and do the math)

29200/1.4641 can be approximated by rounding 1.4641 to 1.5, now we get the approximate value of 19466 (dividing 29200 to 1.5 is much easier)

Note that 1.5>1.4641, so the  actual value  must be a tad greater than 19466. Look at the answer choices, we see that 20,000 is the closest number which is greater than 19466

IMO 20,000

Kinshook · Answer

Asked: 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?

Let the initial investment be x
29200 = x (1.1)^4 
x = 29200/(1.1)^4 = $19944 ~ $20,000

IMO D

Avysar · Answer

First we use the formula 
29200= P ^2^2
Simplifying, we will have P=29200/1.4641
For those you have asked to solve this easily, please note that
29200/1.4<29200/1.46<29200/1.5
20800<P<19000
So 20000
The calculations are approximate values

Posted from my mobile device

HarryStamper · Answer

Yes, there is. I don't know if I am late to the party here.

20% interest on semi-annual basis means 10% every 6 months.

Now use plug-in method and a little of estimation.

Start with option (C)

If the initial investment is $19,000, then interest every six months is 10% of $19,000 and thats $1,900 earned every 6 months. In a period of 2 years, there are 4 instalments of 6 months. So $1,900*4 = $7,600.

Add $7,600 to $19,000 and you will get $26,600. Now compounding will result in a higher number (because interest is compounded), but surely not make up for the $2,600 difference between $29,200 and $26,600.

Try the same approach for option (D) and you will get $28,000 which is closer to $29,200 than is option (c). Option (e) will take you over $29,200.

Hope this shortcut helps.

shailee09 · Answer

The compound interest earned is always little more than the simple interest earned.
so calculating simple interest 
P(1+R*T/100) = 29200
P<21000,
so 20000 should be our answer.

jcaguirre91 · Answer

Here is the fastest way

Being x the original amount of investment

x*(1.1)^4 = 29,200

You do have to do (1.1)^4 which is failry easy = 1.4641

So x*(1.4641) = 29,200 then round 1.4641 to 1.45 (nice number)

x*(1.45) = x*(145/100) divide numerator and denominator by 5 = x*(29/20)

complete equiation x* (29/20) = 29,200 -> x = (29,200*20) / 29

If you round 29,200 to 29,000 you get a really nice operation in which x is 20,000

If you round 1.46 to 1.50 or 1.40 you will get in trouble with the answers later.

dave13 · Answer

VeritasKarishma why in the post above we are not dividing by number of compounding. shouldnt that change the answer when we arent dividing by 2

GMATGuruNY · Answer

We can PLUG IN THE ANSWERS, which represent an approximation of the initial investment.

20% annual interest compounded semi-annually for 2 years --> 10% increase every 6 months --> the investment increases by  1/10 a total of 4 times 
The information in blue suggests that the correct answer is likely to end in four 0's.
When the correct approximation is plugged in, the resulting value after four 10% increases must be close to 29,200.

D: 20,000
The result after four 10% increases:
 20,000 + \frac{20,000}{10} = 20,000 + 2,000 = 22,000 
 22,000 + \frac{22,000}{10} = 22,000 + 2,200 = 24,200 
 24,200 + \frac{24,200}{10} ≈ 24,200 + 2,400 ≈ 26,600 
 26,600 + \frac{26,600}{10} ≈ 26,600 + 2,600 ≈ 29,200 
Success!

D

TarunKumar1234 · Answer

Due to semi annually interest rate compounding, I= 10%, T= 4 years 29200 = P * (1 + 10/100)^4 or, P= 29200*10^4/(121*121)~ 20,000 So, Ans. D.

KarishmaB · Answer

We are dividing by 2.

Annual rate of interest is 20%.

Amount = P(1 + r/200)^2n

29200 = P(1 + 20/200)^2*2 = P(1 + .1)^4 = P(1.1)^4

I know the square of 11 is 121 so 1.1^2 = 1.21. I will approximate to 1.2 which is 6/5

P = 29200 * 5 * 5/(6 * 6) = approx 20,000

Answer (D)

Paras96 · Answer

For compound interest,

A=P(1+R)^T

As per given information,

A= 29200
R=20%/2=10%=0.1 (Because compounded semiannually)
T=2*n=2*2=4 years (Because compounded semiannually)

We get final equation as,

29200=P*(1.1)^4
Solving we get, P = 20000

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