Question:
In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3120
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 = $3120 – $3000 = $120
Thus, Simple Interest = $120
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 × 120/3000 × 2
= 12000/6000
= 2 years (using formula)
Thus, Time (T) = 2 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 = $120 (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 $120, then the time = 1/60 × 120 years
= 1 × 120/60 years
= 120/60 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(4) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(8) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.