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) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(6) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.