Question:
Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7560
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 = $7560 – $4200 = $3360
Thus, Simple Interest = $3360
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 × 3360/4200 × 10
= 336000/42000
= 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) = $4200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3360 (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 $4200
= 10/100 × 4200
= 10 × 4200/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $3360, then the time = 1/420 × 3360 years
= 1 × 3360/420 years
= 3360/420 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?