Question:
James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $5680
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 = $5680 – $4000 = $1680
Thus, Simple Interest = $1680
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 × 1680/4000 × 7
= 168000/28000
= 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) = $4000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $1680 (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 $4000
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = 280
Thus, simple Interest for 1 year = $280
Now,
∵ If the simple Interest is $280, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/280 years
∴ If the simple Interest is $1680, then the time = 1/280 × 1680 years
= 1 × 1680/280 years
= 1680/280 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(4) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.