Question:
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.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8268
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 = $8268 – $5300 = $2968
Thus, Simple Interest = $2968
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 × 2968/5300 × 7
= 296800/37100
= 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) = $5300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2968 (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 = 7% of Principal
= 7% of $5300
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = 371
Thus, simple Interest for 1 year = $371
Now,
∵ If the simple Interest is $371, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/371 years
∴ If the simple Interest is $2968, then the time = 1/371 × 2968 years
= 1 × 2968/371 years
= 2968/371 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.