Question:
Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 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) = 8% per annum
Amount (A) = $9472
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 = $9472 – $6400 = $3072
Thus, Simple Interest = $3072
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 × 3072/6400 × 8
= 307200/51200
= 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) = 8% per annum
Simple Interest = $3072 (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 $3072, then the time = 1/512 × 3072 years
= 1 × 3072/512 years
= 3072/512 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(4) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?