Question:
In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3780
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 = $3780 – $3150 = $630
Thus, Simple Interest = $630
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 × 630/3150 × 4
= 63000/12600
= 5 years (using formula)
Thus, Time (T) = 5 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) = 4% per annum
Simple Interest = $630 (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 = 4% of Principal
= 4% of $3150
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = 126
Thus, simple Interest for 1 year = $126
Now,
∵ If the simple Interest is $126, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/126 years
∴ If the simple Interest is $630, then the time = 1/126 × 630 years
= 1 × 630/126 years
= 630/126 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(6) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.