Question:
Elizabeth took a loan of $4900 at the rate of 10% 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
8
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 10% 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 × 10
= 392000/49000
= 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) = $4900
Rate of Simple Interest (R) = 10% 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 = 10% of Principal
= 10% of $4900
= 10/100 × 4900
= 10 × 4900/100
= 49000/100 = 490
Thus, simple Interest for 1 year = $490
Now,
∵ If the simple Interest is $490, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/490 years
∴ If the simple Interest is $3920, then the time = 1/490 × 3920 years
= 1 × 3920/490 years
= 3920/490 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(3) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(5) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.