Question:
Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10608
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 = $10608 – $6800 = $3808
Thus, Simple Interest = $3808
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 × 3808/6800 × 7
= 380800/47600
= 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) = $6800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3808 (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 = 7% of Principal
= 7% of $6800
= 7/100 × 6800
= 7 × 6800/100
= 47600/100 = 476
Thus, simple Interest for 1 year = $476
Now,
∵ If the simple Interest is $476, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/476 years
∴ If the simple Interest is $3808, then the time = 1/476 × 3808 years
= 1 × 3808/476 years
= 3808/476 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(7) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(8) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.