Question:
Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10595
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 = $10595 – $6500 = $4095
Thus, Simple Interest = $4095
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 × 4095/6500 × 9
= 409500/58500
= 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) = $6500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4095 (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 $6500
= 9/100 × 6500
= 9 × 6500/100
= 58500/100 = 585
Thus, simple Interest for 1 year = $585
Now,
∵ If the simple Interest is $585, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/585 years
∴ If the simple Interest is $4095, then the time = 1/585 × 4095 years
= 1 × 4095/585 years
= 4095/585 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(10) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.