Question:
Mary took a loan of $4100 at the rate of 7% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 7% 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 × 7
= 172200/28700
= 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) = $4100
Rate of Simple Interest (R) = 7% 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 = 7% of Principal
= 7% of $4100
= 7/100 × 4100
= 7 × 4100/100
= 28700/100 = 287
Thus, simple Interest for 1 year = $287
Now,
∵ If the simple Interest is $287, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/287 years
∴ If the simple Interest is $1722, then the time = 1/287 × 1722 years
= 1 × 1722/287 years
= 1722/287 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(2) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(8) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(10) 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.