Question:
Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11040
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 = $11040 – $6900 = $4140
Thus, Simple Interest = $4140
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 × 4140/6900 × 10
= 414000/69000
= 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) = $6900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4140 (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 = 10% of Principal
= 10% of $6900
= 10/100 × 6900
= 10 × 6900/100
= 69000/100 = 690
Thus, simple Interest for 1 year = $690
Now,
∵ If the simple Interest is $690, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/690 years
∴ If the simple Interest is $4140, then the time = 1/690 × 4140 years
= 1 × 4140/690 years
= 4140/690 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(8) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(10) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.