Question:
Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6664
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 = $6664 – $4900 = $1764
Thus, Simple Interest = $1764
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 × 1764/4900 × 6
= 176400/29400
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1764 (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 $4900
= 6/100 × 4900
= 6 × 4900/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $1764, then the time = 1/294 × 1764 years
= 1 × 1764/294 years
= 1764/294 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(6) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.