Question:
James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6240
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 = $6240 – $4000 = $2240
Thus, Simple Interest = $2240
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 × 2240/4000 × 7
= 224000/28000
= 8 years (using formula)
Thus, Time (T) = 8 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 = $2240 (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 $2240, then the time = 1/280 × 2240 years
= 1 × 2240/280 years
= 2240/280 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(9) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.