Question:
In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3654
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $3654 – $3150 = $504
Thus, Simple Interest = $504
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 × 504/3150 × 4
= 50400/12600
= 4 years (using formula)
Thus, Time (T) = 4 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 = $504 (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 $504, then the time = 1/126 × 504 years
= 1 × 504/126 years
= 504/126 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(5) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.