Question:
John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6864
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 = $6864 – $4400 = $2464
Thus, Simple Interest = $2464
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 × 2464/4400 × 8
= 246400/35200
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4400
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2464 (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 $4400
= 8/100 × 4400
= 8 × 4400/100
= 35200/100 = 352
Thus, simple Interest for 1 year = $352
Now,
∵ If the simple Interest is $352, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/352 years
∴ If the simple Interest is $2464, then the time = 1/352 × 2464 years
= 1 × 2464/352 years
= 2464/352 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.