Question:
Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10496
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 = $10496 – $6400 = $4096
Thus, Simple Interest = $4096
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 × 4096/6400 × 8
= 409600/51200
= 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) = $6400
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4096 (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 $6400
= 8/100 × 6400
= 8 × 6400/100
= 51200/100 = 512
Thus, simple Interest for 1 year = $512
Now,
∵ If the simple Interest is $512, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/512 years
∴ If the simple Interest is $4096, then the time = 1/512 × 4096 years
= 1 × 4096/512 years
= 4096/512 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(6) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.