Question:
Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8932
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 = $8932 – $5800 = $3132
Thus, Simple Interest = $3132
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 × 3132/5800 × 6
= 313200/34800
= 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) = $5800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3132 (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 $5800
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = 348
Thus, simple Interest for 1 year = $348
Now,
∵ If the simple Interest is $348, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/348 years
∴ If the simple Interest is $3132, then the time = 1/348 × 3132 years
= 1 × 3132/348 years
= 3132/348 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.