Question:
Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6068
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 = $6068 – $4100 = $1968
Thus, Simple Interest = $1968
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 × 1968/4100 × 6
= 196800/24600
= 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) = $4100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1968 (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 = 6% of Principal
= 6% of $4100
= 6/100 × 4100
= 6 × 4100/100
= 24600/100 = 246
Thus, simple Interest for 1 year = $246
Now,
∵ If the simple Interest is $246, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/246 years
∴ If the simple Interest is $1968, then the time = 1/246 × 1968 years
= 1 × 1968/246 years
= 1968/246 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(4) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(9) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.