Question:
Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9798
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 = $9798 – $6900 = $2898
Thus, Simple Interest = $2898
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 × 2898/6900 × 6
= 289800/41400
= 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) = $6900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2898 (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 $6900
= 6/100 × 6900
= 6 × 6900/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $2898, then the time = 1/414 × 2898 years
= 1 × 2898/414 years
= 2898/414 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(3) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.