Question:
Donald took a loan of $7000 at the rate of 7% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 7% 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 × 7
= 441000/49000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 7% 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 = 7% of Principal
= 7% of $7000
= 7/100 × 7000
= 7 × 7000/100
= 49000/100 = 490
Thus, simple Interest for 1 year = $490
Now,
∵ If the simple Interest is $490, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/490 years
∴ If the simple Interest is $4410, then the time = 1/490 × 4410 years
= 1 × 4410/490 years
= 4410/490 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(8) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.