Question:
Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10620
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 = $10620 – $5900 = $4720
Thus, Simple Interest = $4720
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 × 4720/5900 × 8
= 472000/47200
= 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) = $5900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4720 (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 $5900
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = 472
Thus, simple Interest for 1 year = $472
Now,
∵ If the simple Interest is $472, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/472 years
∴ If the simple Interest is $4720, then the time = 1/472 × 4720 years
= 1 × 4720/472 years
= 4720/472 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(5) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.