Question:
Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11008
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $11008 – $6400 = $4608
Thus, Simple Interest = $4608
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 × 4608/6400 × 8
= 460800/51200
= 9 years (using formula)
Thus, Time (T) = 9 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 = $4608 (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 $4608, then the time = 1/512 × 4608 years
= 1 × 4608/512 years
= 4608/512 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(7) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(9) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.