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

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 = ?

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

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.

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

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

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

First we use the formula
29200= P[1+(20/200)]^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

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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.

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.

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.

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

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!

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.

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)

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