Question:
David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6816
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 = $6816 – $4800 = $2016
Thus, Simple Interest = $2016
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 × 2016/4800 × 6
= 201600/28800
= 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) = $4800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2016 (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 $4800
= 6/100 × 4800
= 6 × 4800/100
= 28800/100 = 288
Thus, simple Interest for 1 year = $288
Now,
∵ If the simple Interest is $288, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/288 years
∴ If the simple Interest is $2016, then the time = 1/288 × 2016 years
= 1 × 2016/288 years
= 2016/288 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.