Question:
Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9512
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 = $9512 – $5800 = $3712
Thus, Simple Interest = $3712
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 × 3712/5800 × 8
= 371200/46400
= 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) = $5800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3712 (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 $5800
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = 464
Thus, simple Interest for 1 year = $464
Now,
∵ If the simple Interest is $464, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/464 years
∴ If the simple Interest is $3712, then the time = 1/464 × 3712 years
= 1 × 3712/464 years
= 3712/464 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(3) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(5) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(9) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.