Question:
In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3339
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 = $3339 – $3150 = $189
Thus, Simple Interest = $189
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 × 189/3150 × 3
= 18900/9450
= 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) = $3150
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $189 (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 $3150
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = 94.5
Thus, simple Interest for 1 year = $94.5
Now,
∵ If the simple Interest is $94.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/94.5 years
∴ If the simple Interest is $189, then the time = 1/94.5 × 189 years
= 1 × 189/94.5 years
= 189/94.5 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) 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.
(2) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.