Question:
In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3240
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $3240 – $3000 = $240
Thus, Simple Interest = $240
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 × 240/3000 × 2
= 24000/6000
= 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) = $3000
Rate of Simple Interest (R) = 2% per annum
Simple Interest = $240 (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 $3000
= 2/100 × 3000
= 2 × 3000/100
= 6000/100 = 60
Thus, simple Interest for 1 year = $60
Now,
∵ If the simple Interest is $60, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/60 years
∴ If the simple Interest is $240, then the time = 1/60 × 240 years
= 1 × 240/60 years
= 240/60 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(3) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(8) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.