Question:
In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3780
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 = $3780 – $3150 = $630
Thus, Simple Interest = $630
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 × 630/3150 × 4
= 63000/12600
= 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) = 4% per annum
Simple Interest = $630 (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 = 4% of Principal
= 4% of $3150
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = 126
Thus, simple Interest for 1 year = $126
Now,
∵ If the simple Interest is $126, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/126 years
∴ If the simple Interest is $630, then the time = 1/126 × 630 years
= 1 × 630/126 years
= 630/126 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(4) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(7) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?