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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