Question:
Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8704
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 = $8704 – $6400 = $2304
Thus, Simple Interest = $2304
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 × 2304/6400 × 6
= 230400/38400
= 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) = $6400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2304 (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 $6400
= 6/100 × 6400
= 6 × 6400/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $2304, then the time = 1/384 × 2304 years
= 1 × 2304/384 years
= 2304/384 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(7) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.