Question:
Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8094
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 = $8094 – $5700 = $2394
Thus, Simple Interest = $2394
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 × 2394/5700 × 6
= 239400/34200
= 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) = $5700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2394 (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 $5700
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = 342
Thus, simple Interest for 1 year = $342
Now,
∵ If the simple Interest is $342, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/342 years
∴ If the simple Interest is $2394, then the time = 1/342 × 2394 years
= 1 × 2394/342 years
= 2394/342 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.