Question:
In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3410
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 = $3410 – $3100 = $310
Thus, Simple Interest = $310
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 × 310/3100 × 2
= 31000/6200
= 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) = $3100
Rate of Simple Interest (R) = 2% per annum
Simple Interest = $310 (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 = 2% of Principal
= 2% of $3100
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = 62
Thus, simple Interest for 1 year = $62
Now,
∵ If the simple Interest is $62, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/62 years
∴ If the simple Interest is $310, then the time = 1/62 × 310 years
= 1 × 310/62 years
= 310/62 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(3) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.
(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(8) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(10) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.