Question:
Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7072
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 = $7072 – $5200 = $1872
Thus, Simple Interest = $1872
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 × 1872/5200 × 6
= 187200/31200
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1872 (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 $5200
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = 312
Thus, simple Interest for 1 year = $312
Now,
∵ If the simple Interest is $312, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/312 years
∴ If the simple Interest is $1872, then the time = 1/312 × 1872 years
= 1 × 1872/312 years
= 1872/312 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(5) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(7) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.