Question:
In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3416
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 = $3416 – $3050 = $366
Thus, Simple Interest = $366
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 × 366/3050 × 4
= 36600/12200
= 3 years (using formula)
Thus, Time (T) = 3 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) = $3050
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $366 (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 $3050
= 4/100 × 3050
= 4 × 3050/100
= 12200/100 = 122
Thus, simple Interest for 1 year = $122
Now,
∵ If the simple Interest is $122, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/122 years
∴ If the simple Interest is $366, then the time = 1/122 × 366 years
= 1 × 366/122 years
= 366/122 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(6) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(8) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?