Question:
Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 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) = 7% per annum
Amount (A) = $10132
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 = $10132 – $6800 = $3332
Thus, Simple Interest = $3332
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 × 3332/6800 × 7
= 333200/47600
= 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) = 7% per annum
Simple Interest = $3332 (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 $3332, then the time = 1/476 × 3332 years
= 1 × 3332/476 years
= 3332/476 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(9) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.