Question:
In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3360
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 = $3360 – $3000 = $360
Thus, Simple Interest = $360
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 × 360/3000 × 3
= 36000/9000
= 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) = 3% per annum
Simple Interest = $360 (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 = 3% of Principal
= 3% of $3000
= 3/100 × 3000
= 3 × 3000/100
= 9000/100 = 90
Thus, simple Interest for 1 year = $90
Now,
∵ If the simple Interest is $90, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/90 years
∴ If the simple Interest is $360, then the time = 1/90 × 360 years
= 1 × 360/90 years
= 360/90 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(2) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(7) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(10) 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.