Question:
John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6864
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 = $6864 – $4400 = $2464
Thus, Simple Interest = $2464
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 × 2464/4400 × 7
= 246400/30800
= 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) = $4400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2464 (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 $4400
= 7/100 × 4400
= 7 × 4400/100
= 30800/100 = 308
Thus, simple Interest for 1 year = $308
Now,
∵ If the simple Interest is $308, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/308 years
∴ If the simple Interest is $2464, then the time = 1/308 × 2464 years
= 1 × 2464/308 years
= 2464/308 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(2) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(4) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.