Question:
James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 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) = 8% per annum
Amount (A) = $6240
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 = $6240 – $4000 = $2240
Thus, Simple Interest = $2240
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 × 2240/4000 × 8
= 224000/32000
= 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) = 8% per annum
Simple Interest = $2240 (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 = 8% of Principal
= 8% of $4000
= 8/100 × 4000
= 8 × 4000/100
= 32000/100 = 320
Thus, simple Interest for 1 year = $320
Now,
∵ If the simple Interest is $320, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/320 years
∴ If the simple Interest is $2240, then the time = 1/320 × 2240 years
= 1 × 2240/320 years
= 2240/320 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(5) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?
(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.