Question:
Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11410
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 = $11410 – $7000 = $4410
Thus, Simple Interest = $4410
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 × 4410/7000 × 9
= 441000/63000
= 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) = $7000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4410 (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 $7000
= 9/100 × 7000
= 9 × 7000/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $4410, then the time = 1/630 × 4410 years
= 1 × 4410/630 years
= 4410/630 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(5) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(6) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.