my first maths questions post (1 Viewer)

DepressedPenguino · May 25, 2015

An amount of $x is invested at a rate of 10% p.a. compound interest, with interest being paid every 6 months. Find in which year the amount resulting is twice the original investment

VBN2470 · May 25, 2015

Is it after 14.545.. (round up to 15) years?

DepressedPenguino · May 25, 2015

VBN2470 said:
Is it after 14.545.. (round up to 15) years?

Unfortunately, i dont have an answer to this question but one of my classmate got 2/3 marks and he got 7 years as his answer.

InteGrand · May 25, 2015

DepressedPenguino said:
An amount of $x is invested at a rate of 10% p.a. compound interest, with interest being paid every 6 months. Find in which year the amount resulting is twice the original investment

$$2x = x(1+r)^n$, where $r=0.05$ and $n$ is the number of 6-month periods. Therefore, $(1+r)^n =2\Rightarrow n \ln (1.05)=\ln 2$ (taking the log of both sides). Hence $n=\frac{\ln 2}{\ln(1.05)}= 14.2066990829$. So the number of years passed is half this, or about 7.1. So the answer is ``in the eighth year''.$

DepressedPenguino · May 25, 2015

InteGrand said:
$$2x = x(1+r)^n$, where $r=0.05$ and $n$ is the number of 6-month periods. Therefore, $(1+r)^n =2\Rightarrow n \ln (1.05)=\ln 2$ (taking the log of both sides). Hence $n=\frac{\ln 2}{\ln(1.05)}= 14.2066990829$. So the number of years passed is half this, or about 7.1. So the answer is ``in the eighth year''.$

Yeah my friend got 7.1 too

This should be right

VBN2470 · May 25, 2015

DepressedPenguino said:
Unfortunately, i dont have an answer to this question but one of my classmate got 2/3 marks and he got 7 years as his answer.

Yep, I should have divided my answer by 2 to get 7.2725.., so it would be at the end of 8 years.

InteGrand · May 25, 2015

VBN2470 said:
Yep, I should have divided my answer by 2 to get 7.2725.., so it would be at the end of 8 years.

I think you did $\frac{\ln 2}{\ln (1.1)}$ ? We need to divide the interest rate by 2 to convert it to a 6-monthly rate though.

VBN2470 · May 25, 2015

^ Never mind, r = 0.05 is correct for each 6 month period, since I realised the 10% rate was a nominal and not an effective rate.

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