Question:
In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3472
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 = $3472 – $3100 = $372
Thus, Simple Interest = $372
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 × 372/3100 × 4
= 37200/12400
= 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) = $3100
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $372 (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 $3100
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = 124
Thus, simple Interest for 1 year = $124
Now,
∵ If the simple Interest is $124, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/124 years
∴ If the simple Interest is $372, then the time = 1/124 × 372 years
= 1 × 372/124 years
= 372/124 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(8) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.