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) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(3) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(10) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.