Question:
William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7700
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 = $7700 – $5000 = $2700
Thus, Simple Interest = $2700
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 × 2700/5000 × 6
= 270000/30000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $5000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2700 (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 $5000
= 6/100 × 5000
= 6 × 5000/100
= 30000/100 = 300
Thus, simple Interest for 1 year = $300
Now,
∵ If the simple Interest is $300, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/300 years
∴ If the simple Interest is $2700, then the time = 1/300 × 2700 years
= 1 × 2700/300 years
= 2700/300 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.