Question:
Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9690
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 = $9690 – $5100 = $4590
Thus, Simple Interest = $4590
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 × 4590/5100 × 10
= 459000/51000
= 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) = $5100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4590 (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 = 10% of Principal
= 10% of $5100
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = 510
Thus, simple Interest for 1 year = $510
Now,
∵ If the simple Interest is $510, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/510 years
∴ If the simple Interest is $4590, then the time = 1/510 × 4590 years
= 1 × 4590/510 years
= 4590/510 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(2) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.