Question:
In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3937.5
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 = $3937.5 – $3150 = $787.5
Thus, Simple Interest = $787.5
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 × 787.5/3150 × 5
= 78750/15750
= 5 years (using formula)
Thus, Time (T) = 5 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) = $3150
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $787.5 (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 $3150
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = 157.5
Thus, simple Interest for 1 year = $157.5
Now,
∵ If the simple Interest is $157.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/157.5 years
∴ If the simple Interest is $787.5, then the time = 1/157.5 × 787.5 years
= 1 × 787.5/157.5 years
= 787.5/157.5 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(10) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.