Question:
Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $5822
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 = $5822 – $4100 = $1722
Thus, Simple Interest = $1722
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 × 1722/4100 × 6
= 172200/24600
= 7 years (using formula)
Thus, Time (T) = 7 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 = $1722 (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 $1722, then the time = 1/246 × 1722 years
= 1 × 1722/246 years
= 1722/246 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(7) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.