Question:
Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8820
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 = $8820 – $4900 = $3920
Thus, Simple Interest = $3920
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 × 3920/4900 × 8
= 392000/39200
= 10 years (using formula)
Thus, Time (T) = 10 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) = 8% per annum
Simple Interest = $3920 (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 $4900
= 8/100 × 4900
= 8 × 4900/100
= 39200/100 = 392
Thus, simple Interest for 1 year = $392
Now,
∵ If the simple Interest is $392, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/392 years
∴ If the simple Interest is $3920, then the time = 1/392 × 3920 years
= 1 × 3920/392 years
= 3920/392 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(4) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.