Question:
In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3286
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 = $3286 – $3100 = $186
Thus, Simple Interest = $186
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 × 186/3100 × 2
= 18600/6200
= 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) = 2% per annum
Simple Interest = $186 (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 = 2% of Principal
= 2% of $3100
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = 62
Thus, simple Interest for 1 year = $62
Now,
∵ If the simple Interest is $62, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/62 years
∴ If the simple Interest is $186, then the time = 1/62 × 186 years
= 1 × 186/62 years
= 186/62 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(3) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(10) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?