Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11868
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 = $11868 – $6900 = $4968
Thus, Simple Interest = $4968
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 × 4968/6900 × 9
= 496800/62100
= 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) = $6900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4968 (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 = 9% of Principal
= 9% of $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $4968, then the time = 1/621 × 4968 years
= 1 × 4968/621 years
= 4968/621 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) 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?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.