Question:
In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3875
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 = $3875 – $3100 = $775
Thus, Simple Interest = $775
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 × 775/3100 × 5
= 77500/15500
= 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) = 5% per annum
Simple Interest = $775 (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 $775, then the time = 1/155 × 775 years
= 1 × 775/155 years
= 775/155 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(2) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.