3 Views

Question : A sum of money placed at compound interest doubles itself in 5 years. In how many years would it amount to eight times itself at the same rate of interest?

Option 1: 10 years

Option 2: 15 years

Option 3: 7 years

Option 4: 20 years


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 2nd Jan, 2024

Correct Answer: 15 years


Solution : By applying the formula: Amount = P[$(1+\frac{r}{100})^n$] where P is principal, $r$ is the rate of interest compounded annually for $n$ years.
Let the sum be $x$, then:
Amount = $x(1+\frac{r}{100})^5 = 2x$
⇒ $(1+\frac{r}{100})^5 = \frac{2x}{x}=2$
⇒ $(1+\frac{r}{100})=2^\frac{1}{5}$
Now, the sum becomes 8 times after $n$ years, then:
$x(1+\frac{r}{100})^n = 8x$
⇒ $(1+\frac{r}{100})^n = \frac{8x}{x}=8=2^3$
⇒ $2^\frac{n}{5} = 2^3$
Thus, $n$ = 5 × 3 = 15 years
Hence, the correct answer is 15 years.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
GRE ® Registrations 2024
Apply
Apply for GRE® Test now & save 10% with ApplyShop Gift Card | World's most used Admission Test for Graduate & Professional Schools
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books