Question:
John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8360
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 = $8360 – $4400 = $3960
Thus, Simple Interest = $3960
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 × 3960/4400 × 10
= 396000/44000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% per annum
Simple Interest = $3960 (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 = 10% of Principal
= 10% of $4400
= 10/100 × 4400
= 10 × 4400/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $3960, then the time = 1/440 × 3960 years
= 1 × 3960/440 years
= 3960/440 = 9 years
Thus, time (T) = 9 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 $10608 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(9) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?