Question:
Mark took a loan of $6800 at the rate of 7% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9656
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 × 7
= 285600/47600
= 6 years (using formula)
Thus, Time (T) = 6 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 = $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 = 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 $2856, then the time = 1/476 × 2856 years
= 1 × 2856/476 years
= 2856/476 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.