Question:
James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $5960
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 = $5960 – $4000 = $1960
Thus, Simple Interest = $1960
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 × 1960/4000 × 7
= 196000/28000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $1960 (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 = 7% of Principal
= 7% of $4000
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = 280
Thus, simple Interest for 1 year = $280
Now,
∵ If the simple Interest is $280, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/280 years
∴ If the simple Interest is $1960, then the time = 1/280 × 1960 years
= 1 × 1960/280 years
= 1960/280 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(2) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) 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.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(5) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(10) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.