Question:
William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7800
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 = $7800 – $5000 = $2800
Thus, Simple Interest = $2800
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 × 2800/5000 × 7
= 280000/35000
= 8 years (using formula)
Thus, Time (T) = 8 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) = 7% per annum
Simple Interest = $2800 (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 $5000
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = 350
Thus, simple Interest for 1 year = $350
Now,
∵ If the simple Interest is $350, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/350 years
∴ If the simple Interest is $2800, then the time = 1/350 × 2800 years
= 1 × 2800/350 years
= 2800/350 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?