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Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n?
- a)50 years
- b)25 years
- c)12 years 6 months
- d)37 years 6 months
- e)40 years
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Braun invested a certain sum of money at 8% p.a. simple interest for n...
Step 1: Assume initial investment (Principal) and compute final value (amount) after n years
For any assumed principal, the number of years is going to remain the same because the amount is expressed as ‘x’ times the principal i.e., 4 times in this case.
Let us assume the initial investment (principal) by Braun to be $100.
Amount = 4 × Principal = $400
Amount = Principal + Simple Interest
Therefore, the Simple Interest earned = 400 - 100 = $300.
Step 2: Find the number of years n
Substitute assumed value of principal and the corresponding interest earned, and rate of interest in equation 1.
Or 8n = 300
Or n = 37.5 years
Any amount, when invested for 37.5 years at 8% per annum simple interest would become 4 times the initial value.
Or 8n = 300
Or n = 37.5 years
Any amount, when invested for 37.5 years at 8% per annum simple interest would become 4 times the initial value.
Alternative Method:
Find the number of years required to double the initial amount (principal).
When the initial investment doubles, the interest earned is the same as the initial investment (principal).
So, if principal = 100, interest earned = 100 and r = 8%.
So, n = 100/8 = 12.5 years.
When the initial investment doubles, the interest earned is the same as the initial investment (principal).
So, if principal = 100, interest earned = 100 and r = 8%.
So, n = 100/8 = 12.5 years.
Initial investment of $100 becomes $400 after earning an interest of $300.
To earn $100 interest it took 12.5 years. Hence, it will take 3 × 12.5 = 37.5 years to earn $300 interest.
To earn $100 interest it took 12.5 years. Hence, it will take 3 × 12.5 = 37.5 years to earn $300 interest.
Choice D is the correct answer.
Most Upvoted Answer
Braun invested a certain sum of money at 8% p.a. simple interest for n...
Understanding the Problem:
Given that Braun invested a certain sum of money at 8% p.a. simple interest for n years and at the end of n years, he got back 4 times his original investment.
Solution:
Let's assume Braun invested $100 initially.
After n years, he received back 4 times his original investment, which is $400.
The interest earned on the investment is $400 - $100 = $300.
Calculating the Time Period:
Using the formula for simple interest:
Simple Interest = Principal x Rate x Time
$300 = $100 x 8% x n
$300 = $8n
n = $300 / $8 = 37.5 years
Therefore, the value of n is 37.5 years, which can be written as 37 years 6 months.
So, the correct answer is option D) 37 years 6 months.
Given that Braun invested a certain sum of money at 8% p.a. simple interest for n years and at the end of n years, he got back 4 times his original investment.
Solution:
Let's assume Braun invested $100 initially.
After n years, he received back 4 times his original investment, which is $400.
The interest earned on the investment is $400 - $100 = $300.
Calculating the Time Period:
Using the formula for simple interest:
Simple Interest = Principal x Rate x Time
$300 = $100 x 8% x n
$300 = $8n
n = $300 / $8 = 37.5 years
Therefore, the value of n is 37.5 years, which can be written as 37 years 6 months.
So, the correct answer is option D) 37 years 6 months.
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