Leandro invests P dollars for n years into a bank account that compounds annually at the rate of r%.

Quantity A

The value of \frac{r}{100}

for the accumulated interest to equal P

Quantity B

2^{\frac{1}{n}}

I simplified it by considering as simple interest problem

\frac{r}{100}*P*n=P

\frac{r}{100}=\frac{1}{n}

we are now comparing 1/n and 2^{\frac{1}{n}}. 2^{\frac{1}{n}} will be greater. As n increase, 1/n will converge to 0 while 2^{\frac{1}{n}} will converge to 1.

Is this solution correct or just luck. Let me know your solution for this problem.

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thanks. I tried this way also but I did a mistake

May I ask the source of this question?

you can see them in solve quants problems under video solution tag.

Leandro invests PP dollars for nn years into a bank account that compounds annually at the rate of r%r%.

Quantity A

The value of \frac{r}{100}

100

r

for the accumulated interest to equal PP

Quantity B

2^{\frac{1}{n}}2

n

1

Can you reformat the question, it doesn’t make much sense

I don’t understand… isn’t the formula for compound interest written in this way:

Where is the “t” ?

Here t= time period

n= how the time period is distributed

For example if an amount is compounded for every 6 months and the annual rate is 8% what would be the intrest for 3 years

How would I solve this?

So annually it’s 8%, so for 6 months it would be 4% so now my r =4 and it’s compounded for 3 years how many 6 months are there in 3 years 2*3=6

So n how the time period is distributed and t is the total time to which it is distributed.

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I can see the t - it’s just a difference in the notation used.

How do we solve this one?

If you look at compound interest formula :

A=P(1+\frac{r}{n})^{nt}

A = future value of the investment

P = initial value / initial investment/Principal

r = interest rate per year

t = time (in years)

n = number of compounding periods per year

But if you look at **Qty A** its not telling us to calculate the future value (A) but its asking how much Compound Interest/C.I. (accumulated interest) we have and setting it equal to initial investment /principal(P).

Now, to do that you can just subtract the Principal from A to get accumulated Interest/C.I.

OR

C.I. = P\times[(1+\frac{r}{n})^{t\times n}-1]

And replace C.I. with P (because QtyA tell us to equate it to P), thus the formula become:-

P= P\times[(1+\frac{r}{n})^{t\times n}-1]

Once you have set up the equation , you can solve it like how @prakithgre has done it above.

https://forums.gregmat.com/t/leandro-invests-p-dollars/11738/2?u=kremlinofficial

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