Question:
James took a loan of $4000 at the rate of 6% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 6% 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 × 6
= 168000/24000
= 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) = $4000
Rate of Simple Interest (R) = 6% 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 = 6% of Principal
= 6% of $4000
= 6/100 × 4000
= 6 × 4000/100
= 24000/100 = 240
Thus, simple Interest for 1 year = $240
Now,
∵ If the simple Interest is $240, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/240 years
∴ If the simple Interest is $1680, then the time = 1/240 × 1680 years
= 1 × 1680/240 years
= 1680/240 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(4) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(10) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.