Question:
In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3750
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 = $3750 – $3000 = $750
Thus, Simple Interest = $750
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 × 750/3000 × 5
= 75000/15000
= 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) = $3000
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $750 (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 $3000
= 5/100 × 3000
= 5 × 3000/100
= 15000/100 = 150
Thus, simple Interest for 1 year = $150
Now,
∵ If the simple Interest is $150, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/150 years
∴ If the simple Interest is $750, then the time = 1/150 × 750 years
= 1 × 750/150 years
= 750/150 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(2) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(10) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.