Question:
In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3720
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 = $3720 – $3100 = $620
Thus, Simple Interest = $620
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 × 620/3100 × 5
= 62000/15500
= 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) = $3100
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $620 (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 = 5% of Principal
= 5% of $3100
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = 155
Thus, simple Interest for 1 year = $155
Now,
∵ If the simple Interest is $155, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/155 years
∴ If the simple Interest is $620, then the time = 1/155 × 620 years
= 1 × 620/155 years
= 620/155 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(10) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.