Question : In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
Correct Answer 2
Solution & Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3300
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $3300 – $3000 = $300
Thus, Simple Interest = $300
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 300/3000 × 5
= 30000/15000
= 2 years (using formula)
Thus, Time (T) = 2 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $3000
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $300 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 5% of Principal
= 5% of $3000
= 5/100 × 3000
= 5 × 3000/100
= 15000/100 = 150
Thus, simple Interest for 1 year = $150
Now,
∵ If the simple Interest is $150, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/150 years
∴ If the simple Interest is $300, then the time = 1/150 × 300 years
= 1 × 300/150 years
= 300/150 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.