Question:
Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9656
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 = $9656 – $6800 = $2856
Thus, Simple Interest = $2856
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 × 2856/6800 × 6
= 285600/40800
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2856 (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 $6800
= 6/100 × 6800
= 6 × 6800/100
= 40800/100 = 408
Thus, simple Interest for 1 year = $408
Now,
∵ If the simple Interest is $408, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/408 years
∴ If the simple Interest is $2856, then the time = 1/408 × 2856 years
= 1 × 2856/408 years
= 2856/408 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(2) 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?
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(6) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.